Professor Minyue Fu

In this chapter, the distributed bisection algorithm (DBA) is presented for the economic dispatch problem in a smart grid scenario, with the goal to minimize the aggregated cost of a network of generators, which cooperatively furnish a given amount of power within their individual capacity constraints. The DBA adopts the method of bisection, and is based on a consensus-like iterative method, with no need for a central decision maker or a leader node. Under strong connectivity conditions and allowance for local communications, it is shown that the iterative solution converges to the globally optimal solution. Furthermore, two stopping criteria are presented for the practical implementation of the proposed algorithm, for which sign consensus is defined.

This chapter considers the quantized linear quadratic Gaussian (QLQG) control problem, which is generalized from the classical LQG problem but with the constraint that the feedback signal is quantized by a fixed-rate quantizer. It turns out that the well-known separation principle for LQG control fails to generalize to QLQG, and this is caused by the fact that minimizing the quantization error at each time instant separately does not lead to a minimum cost globally. Here we consider the QLQG problem for a scalar system and present an adaptive quantization scheme. Using this scheme, we show that the quantization distortion order is R2-2R for a large bit rate R. This means that the separation principle holds approximately when the bit rate is sufficient. More importantly, this adaptive quantization scheme guarantees mean-square stability for the closed-loop system.

This paper presents a practical control approach for a cart-pole system, focusing on system identification, friction compensation, and rail limit management. First, a system model is developed, incorporating both kinetic and static friction effects. During the swing-up phase, system parameters are estimated to enhance control accuracy. An energy control method incorporating logarithmic barrier functions (LBF) is then used to swing the pole upright, ensuring the cart remains within the physical boundaries of the rail. Finally, a Linear Quadratic Regulator (LQR) is designed to stabilize the pole in the upright position. All methods are validated on a real hardware system, demonstrating the effectiveness of the proposed parameter identification and control techniques in achieving stable and safe control of the cart-pole system.

Belief propagation (BP) is a well-celebrated iterative optimization algorithm in statistical learning over network graphs with vast applications in many scientific and engineering fields. This paper studies a fundamental property of this algorithm, namely, its convergence behaviour. Our study is conducted through the problem of distributed state estimation for a networked linear system with additive Gaussian noises, using the weighted least-squares criterion. The corresponding BP algorithm is known as Gaussian BP. Our main contribution is to show that Gaussian BP is guaranteed to converge, under a mild regularity condition. Our result significantly generalizes previous known results on BP's convergence properties, as our study allows general network graphs with cycles and network nodes with random vectors. This result is expected to inspire further investigation of BP and wider applications of BP in distributed estimation and control.

This paper studies the formation control problem for a leader-follower network in 3D. The objective is to control the agents to form a globally rigid formation, for which the sensing graph is directed and switching while the communication graph is undirected and switching. Under such a setup, a barycentric coordinate based approach is proposed for the design of formation control laws ensuring global convergence. A necessary and sufficient graphical condition is obtained to guarantee that the followers converge to form a globally rigid formation together with the leaders. By this approach, the formation of the whole group, namely, the orientation, translation and formation scale, can be reconfigured by the leaders.

This paper proposes a switching control strategy for formation maneuvering control of multi-agent systems with guaranteed collision avoidance and connectivity maintenance properties. The control strategy consists of three parts: formation maneuvering, collision avoidance, and connectivity maintenance control. We adopt the idea of using complex Laplacian for formation maneuvering control, which gives rise to one degree of freedom in scaling the size of the achievable formations and thus enables collision avoidance and connectivity maintenance possible in the meantime. Simulation results are provided to demonstrate the effectiveness of the control strategy.

The economic dispatch problem (EDP) is of vital importance in the operation and control of power systems. In this paper, we consider the extended EDP that takes into account transmission losses and propose a distributed algorithm based on the average consensus algorithm and the bisection method. We assume that the total transmission losses can be represented by the B matrix loss formula, and the communication network between generators (nodes) is a connected undirected graph. A leader node is used to broadcast the total demand information by communicating with merely a small part of the nodes. Our algorithm is distributed in the sense that the nodes conduct local computations and communicate with their neighbors. Simulation results are given to show the performance of our algorithm.

Plug-in electric vehicles (PEVs) are becoming increasingly popular because of the environmental and economic benefits. However, high penetration of PEVs may overload the distribution network. In this paper, we propose a decentralized PWM-based algorithm to coordinate PEV charging. We first formulate the PEVs charging coordination problem as an optimization problem, with the objective to flatten the total demand curve as much as possible. Then, we design the control algorithm in two stages. In the first stage, we adopt the the water-filling-based algorithm proposed in our previous study, assuming the charging rate of PEVs takes a continuous value. In the second stage, the assumption is dropped by utilizing the pulse-width modulation (PWM) principle. The moving horizon idea is also introduced to alleviate the errors due to inaccurate forecast and quantization, as well as to tackle the random arrival time of PEVs. Moreover, each PEV only needs to calculate its own power allocation, and hence its implementation requires low computational capacity. Numerical simulations are given to demonstrate the effectiveness of our algorithm.

This paper is concerned with the stabilization problem for discrete-time stochastic systems with multiplicative noise and multiple input delays. Our approach is based on a reduction technique, by which the system under consideration is converted into a delay-free system. The necessary and sufficient stabilization condition for stabilization and the associated feedback controller are characterized via a generalized Riccati equation.

This paper focus on the consensusability of high-order multi-agent systems (MASs) with uniform constant communication delay in an undirected network. We show that N agents achieve consensus if and only if N - 1 time-delay subsystems associated with the eigenvalues of the Laplacian matrix are simultaneously asymptotically stable. By employing a linear matrix inequality (LMI) method, we present a sufficient condition for MASs to reach consensus. Also we consider the consensus condition of first-order integrator system by using frequency domain analysis.

This paper studies a dynamic state estimation problem for power systems, which can be seen as the quasi-static systems. The state vector of each subsystem (called node) in power networks is expressed by measurements. Based on a distributed maximum a posteriori (MAP) estimation technique, a fully distributed state estimation method is presented to update the local state at each time instant. Also, the assumption of local observability of every node is no longer needed. Tests on the IEEE 118-bus system are used to show the performance of the proposed approach and compare its results with a centralized state estimation method providing the optimal state estimate for the entire power networks, a local state estimation method using the edge measurements as the local measurements to estimate its local state, and a distributed static state estimation algorithm.

The purpose of this paper is to study stabilization problem of linear time-invariant systems subject to stochastic multiplicative uncertainties and time delays. We consider a structured multiplicative perturbation which consists of static, zero-mean stochastic processes and we assess the stability of system based on mean-square criteria. The mean-square stabilization problem for multi-input multi-output systems generally requires solving an optimization problem involving the spectral radius of a certain closed loop transfer function matrix. This problem in general is non-convex and by and large unresolved, only approximate solutions are available based on numerical algorithms resembling to the D-K iteration for µ-synthesis. Our main contributions include the fundamental conditions, both necessary and sufficient, which insure that the multi-input multi-output minimum phase systems can be stabilized by output feedback in the mean-square sense. We provide a complete, computationally efficient solution in the form of a generalized eigenvalue problem readily solvable by means of linear matrix inequality optimization. For conceptual insights, limiting cases are analyzed in depth to characterize and quantify explicitly how the directions of unstable poles may affect the mean-square stabilizability of multi-input multi-output systems.

In this paper, we propose a distributed algorithm for the dynamic economic dispatch problem (DEDP) in a smart grid scenario. Different from the static economic dispatch problem (SEDP), the DEDP aims at minimizing the aggregate operating costs of a group of generators over a time period with ramp rate constraints. The proposed algorithm is based on the average consensus algorithm on undirected graphs and the alternating direction method of multipliers (ADMM). Our algorithm is distributed in the sense that no leader or master nodes are needed, while all the nodes (generators) conduct local computation and merely communicate with their neighbors. Convergence analysis shows that the proposed algorithm converges to the optimal solution.

This paper studies a state estimation problem for a networked dynamic system characterized by a communication graph. A new distributed state estimation method is based on a distributed MAP (maximum a posteriori) estimation algorithm for each node to update its local state. This distributed method is applied to the state estimation problem for a large power network and illustrated using the IEEE 118-bus system. It is shown that the performance of this method is close to that given by a centralized Kalman filtering approach and much better than that given by a local Kalman filtering approach, yet the computational complexity and communication load of the proposed method are low for each node, making the method scalable for large-sized networked systems.

The paper improves the cross-correlation method about the condition monitoring for train suspension systems. The faults of both the spring and the damper are discussed and the improved technique helps quantify the result of the detection in a great accuracy. A side-view model of the vehicle is employed and the simulation verifies the effectiveness of this method.

Plug-in hybrid electric vehicles (PHEV) tend to become more widespread in the next decades. However, large penetration of PHEVs will overload the distribution system. In smart grid, the charging of PHEVs can be controlled to reduce the peak load, which is known as demand side management (DSM). In this paper, we focus on the impact of PHEV charging on low-voltage transformers. The objective is to flatten the load curve of low-voltage transformers, while each consumer's requirement for their PHEV to be charged to the required level by their specified time is satisfied. We first formulate it as a convex optimization problem and then propose a distributed water-filling-based algorithm to solve it. Proofs of optimality and numerical simulations are given to demonstrate the effectiveness of our algorithm.

In the recent years, condition monitoring of the train suspension system draws a lot of attention because it acts as the guardian to ensure the safety of the train and provides more information for the overhaul. Meanwhile, it makes the train runs steadily and reduces the operating costs. This article focuses on the identification of the train suspension parameters using a cross-correlation technique. We show that the new method can effectively estimate the coefficients of both the spring and the damping coefficients. Simulation results are presented to show the effectiveness of this method.

This paper studies optimal regulation problem for networked linear discrete-time systems with fading channel. The uncertainties in fading channels are modeled as multiplicative noises. The regulation performance is measured by a quadratic function. The optimal state feedback is designed by the mean-square stabilization solution to a modified Algebraic Riccati equation (MARE). The necessary and sufficient condition to the existence of the mean-square stabilization is presented in terms of the inherent characterizations of the systems. It is a nature extension for the result in standard optimal discrete-time linear quadratic regulation (LQR) problem. We also show that this optimal state feedback design problem is an eigenvalue problem (EVP). And then a design algorithm is developed for this optimal control problem.

The paper studies the formation merging problem for a leader-follower network. That is, how to control a team of agents called followers so that they are merged with a team of agents called leaders to form a larger globally rigid formation. Under the premise that a group of leaders move in a globally rigid formation with their synchronized velocity known to the followers, we show that the followers can asymptotically merge themselves to the formation for arbitrarily initial configurations. Each follower selects its neighbors and also its control law according to the target formation they aim to achieve and thus it allows directed and time-varying switching topologies. It is shown that a globally rigid formation can be merged asymptotically for the leader-follower network in a setup with directed and time-varying graphs if and only if every follower frequently has a joint path from at least a leader.

© 2014 IEEE.This paper proposes a simple, distributed control protocol for multi-agent systems with relative sensing capability over a directed network to achieve an affine formation. In contrast to the linear consensus protocol, the control protocol in this paper takes both positive and negative weights that partially encode the target formation shape and is thus able to achieve a formation pattern rather than just consensus. Having possibly negative weights in a graph, the associated Laplacian is called the generalized Laplacian. The connection between the generic rank property of the generalized Laplacian and the connectivity of a directed graph is established, based on which a necessary and sufficient graphical condition is developed to ensure the emergence of an affine formation by the proposed distributed control protocol.

© 2014 IEEE.This paper studies the formation maneuvering control problem for a network of agents with the objective of achieving a desired group formation shape and a constant over-all group maneuvering velocity. A fully distributed approach is developed to solve the problem. That is, a control law is proposed for each agent in the network, with its parameters capable of being designed in a distributed manner, and is implementable locally via relative sensing and communication with neighbors. Necessary and sufficient conditions regarding a critical control parameter are obtained to guarantee the globally asymptotic convergence of the overall system for both the single-integrator kinematics case and the double-integrator dynamics case.

This paper studies the problem of countering the fluctuations of renewable power supply in smart grid. A fully distributed algorithm to control a network of thermostatically controlled loads (TCLs) is proposed to match, in real time, the aggregated power consumption of the TCLs and the forecast power supply. The algorithm is developed by converting the control problem into a consensus problem of individual utility functions. We then show that the problem is equivalent to a convex optimization problem and an algorithm based on distributed bisection method is presented to solve the problem. The proposed algorithm converges fast and is fully distributed, requiring only local information for each TCL and limited communication with neighboring TCLs, yet the available power supply is fairly dispatched among different TCLs. A numerical example is given to illustrate the effectiveness of the algorithm when applied to a network of variable-frequency air-conditioners (VFACs).

© 2014 IEEE.Economic dispatch problem (EDP) is an important optimization problem in power systems, aiming at minimizing the aggregate cost of a group of power generators, which cooperatively generate a given amount of power within their individual capacity constraints. In this paper, we present an average consensus based bisection approach for the EDP with quadratic cost functions, which is fully distributed and especially desirable in a smart grid scenario. Under the connected topology condition, we show that the proposed iterative solution converges to the globally optimal solution of EDP, without the need for a central decision maker or a leader node. Finally, numerical simulation based on the IEEE 14-bus system is given to show the performance of the approach.

In this paper we investigate the stability of discrete-time linear time-invariant systems subject to finite-level logarithmic quantized feedback. Both state feedback and output feedback are considered. We develop an LMI approach to estimate, for a given controller and a given finite-level quantizer, a set of admissible initial states and an associated attractor set in a neighborhood of the origin such that all state trajectories starting in the first set will converge to the attractor in a finite time and will never leave it. Furthermore, when these two such sets are a priori specified, we develop sufficient conditions for designing a suitable state or output feedback controller, along with a finite-level logarithmic quantizer.

The paper studies the formation control problem for distributed robot systems. It is assumed each robot only has access to local sensing information (i.e. The relative positions and IDs of its neighbors). Taking into consideration physical sensing constraints (e.g. limited sensing range) and the motion of the robots over time, it may be noted that the sensing graph for the system is directed and time-varying. This presents a challenging situation for formation control. As an initiative attempt to study this challenging situation, we suppose the sensing graph switches among a family of graphs with certain connectivity properties, under which a switching linear control law is then proposed. We show that for arbitrary dwell times or average dwell times, the proposed control law with properly designed control parameters can ensure global convergence to a desired formation shape. The proposed formation control law can be implemented in a distributed manner while the design of certain control parameters requires some global information.

We study a networked state estimation problem for a linear system with multiple sensors, each of which transmits its measurements to a central estimator via a lossy communication network for computing the minimum mean-square-error (MMSE) state estimate. Under a general Markov packet loss process, we establish necessary and sufficient conditions for the stability of the estimator for any diagonalizable system in the sense that the mean of the state estimation error covariance matrix is uniformly bounded. For the second-order systems under an i.i.d. packet loss model, the stability condition is expressed as a simple inequality in terms of open-loop poles and the packet loss rate.

In this paper, the state estimation problem for continuous-time linear systems with two types of sampling is considered. First, the optimal state estimator under periodic sampling is presented. Then the state estimator with event-based updates is designed, i.e., when an event occurs the estimator is updated linearly by using the measurement of output, while between the consecutive event times the estimator is updated by minimum mean-squared error criteria. The average estimation errors under both sampling schemes are compared quantitatively for first and second order systems, respectively. A numerical example is given to compare the effectiveness of two state estimators.

A recently proposed Bayesian tracking procedure for sensor networks approximates the update equation, which involves non-linear measurements, with a simple equation using the maximum likelihood (ML) estimate of the unknown state. This approach permits a numerically efficient implementation of the tracking procedure, and is suitable for a distributed implementation. In this paper we study the extent to which this approach approximates the theoretical Bayesian solution. We provide conditions to guarantee that the approximation becomes asymptotically exact, as the number of nodes becomes large. This result is relevant in applications where each sensor obtains a measurement with limited information about the state, but a large number of sensors is available. We apply our result to a case study, and present numerical simulations, showing that the approximation error becomes negligible for a relatively small number of nodes.

This paper studies optimal control designs for networked linear discrete-time systems with quantization effects and/or fading channel. The quantization errors and/or fading channels are modeled as multiplicative noises. The H2 optimal control in mean-square sense is formulated. The necessary and sufficient condition to the existence of the mean-square stabilizing solution to a modified algebraic Riccati equation (MARE) is presented. The optimal H2 control via state feedback for the systems is designed by using the solution to the MARE. It is a nature extension for the result in standard optimal discrete-time H2 state feedback design. It is shown that this optimal state feedback design problem is eigenvalue problem (EVP) and the optimal design algorithm is developed. © 2014 IEEE.

The paper presents a linear approach for formation control of multiple autonomous agents in d-dimensional space. The generalized notion of graph Laplacian, associated to a graph with possibly negative weights on the edges, is introduced aiming to solve the formation problem of controlling a network of point agents to form a given pattern (including rotation, translation, and scaling). By assuming the number of agents is larger than d + 1, we derive that a linear distributed control law exists for this purpose if and only if certain algebraic conditions hold (or equivalently, the graph is globally rigid). Next, it is shown that the generalized graph Laplacian used to stabilize the formations can be obtained by solving a convex optimization problem. Further results are also provided to reveal the conditions under which the attained formations are congruent to or just translations of the desired one. © 2013 IEEE.

This paper presents a reset state estimator to improve the position estimation for motion control systems with sensor quantization. The reset scheme is guided by the idea that the actual output is known exactly to be at the mid-point of the two consecutive quantizer levels and is within the range of a quantizer level bounded by half of quantization step size. Hence, using this information to update the estimated state can give a better estimation under the influence of disturbance and quantization noise. We also show that the reset scheme will not destroy the stability of a baseline estimator system. The reset state estimator is applied to a linear motor control system with an optical encoder. Simulation and experiment demonstrate that the reset state estimator can achieve smaller position estimation error and more accurate tracking accuracy than those of a standard state estimator. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

In this paper we consider the problem of state estimation for linear dynamic systems using quantized measurements. This problem arises when state estimation needs to be done using information transmitted over a digital communication channel. We investigate how to design the quantizer and the estimator jointly. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

We analyze a turbo equalization system that combines Maximum a Posteriori Probability (MAP) equalization with irregular turbo codes. Our goal is to approach the information capacity limit for severe Inter-Symbol Interference (ISI) channels. To this end, we optimize the degree profile of irregular turbo codes by maximizing the minimum distance between the mutual information transfer functions for the MAP equalizer and decoder. We show that turbo equalizers employing such optimized irregular turbo codes can approach the information capacity limit of some severe ISI channels within 0.75 dB. © 2007 IEEE.

Synchronization of multi-stage is a typical system widely used in manufacturing industry which provides many challenges and opportunities for applications of motion control. This paper presents a new synchronization control approach which stabilizes the synchronizing errors dynamics of multi-stage. The system targeted in this paper consists of two stages with serial connection. For the master stage, the proposed control technique is used to follow a given motion planning, and for the slave stage, a nest switching method is introduced to the proposed controller for improving the synchronization performance with small control input to avoid high feedback gain. The switching control applies different control gains when the system states lie in different regions. The regions can be described by the nested ellipsoids with outer ellipsoids corresponding to the looser performance bounds and the inner ones to tighter bounds in the synchronization error regions. Several simulations will be demonstrated carried on a higher order experimentally validated model with a manufacturing industry background.

This paper studies the problem of quantized feedback control for sampled-data systems which employ a quantizer to transmit feedback signals at a given sampling rate. The so-called static (memoryless) quantizers are considered. Given a continuous-time system, the design objective is to stabilize the system or to achieve certain performance using the coarsest quantization density. We study the possible advantages of over-sampling where the input/output signals of the system are sampled at a faster rate than the quantizer. Our first result is for stabilization, and it shows that the coarsest quantization density achievable using quantized state feedback can be generically achieved using output feedback with any over-sampling ratio. Our second result provides a solution to the quantized feedback H8 problem for both with and without over-sampling Copyright © 2005 IFAC.

A novel direct approach for modeling continuous-time stochastic processes is proposed in this paper. First the observed data is passed through an input-to-state filter and the covariance of the output state is computed. The properties of the state covariance matrix is then exploited to estimate the positive real spectrum of the observed data at a set of prescribed points on the right half plane. Finally, the continuous-time parameters are obtained from the positive real spectrum estimates by solving a Nevanlinna-Pick interpolation problem. The estimated model is stable. The analytical results are illustrated using numerical simulations. Copyright © 2005 IFAC.

in this paper, we study the problem of robust regulation for a class of linear uncertain systems which admit the so-called Recursive Augmentation Structure. This structure is known to be quadratically stabilizable and is a rich class, including lowertriangular and upper-triangular structures (which correspond to the so-called backstepping and forwarding in nonlinear control) as special cases. The results of this paper provide conditions on the Recursive Augmentation Structure under which robust regulation can be achieved. Our work differs from existing work on robust regulation for linear systems in the sense that we allow large uncertainties in the system. Our work is also expected to be useful in searching for possible new structures for regulation control of nonlinear systems. Copyright © 2005 IFAC.

We consider the standard (point-wise) linear channel model for MIMO wireless systems in terms of a continuous operator channel. We show analytically that the point-wise representation over-estimates the (true) modal connection strengths and produces artificially distorted channel singular values. Analytic results are compared with simulations for simple channel models and the convergence of the point-wise model toward the continuous model is shown. © 2004 IEEE.

Integral quadratic constraints (IQC) arise in many optimal and/or robust control problems. The IQC approach can be viewed as a generalization of the classical multiplier approach in the absolute stability theory. In this paper, we study the relationship between the two approaches for robust stability analysis. The key result shows that for many applications, the existence of an IQC is equivalent to the existence of a multiplier. Because the multiplier approach is typically simpler and more intuitive, this result suggests that the multiplier approach may be more useful than the IQC approach in many applications.

This paper discusses discrete Hammerstein model identification using blind system identification approach. By sampling faster at the output for the sampled Hammerstein systems, it is shown that identification of the linear part can be achieved based only on the output measurements that makes Hammerstein model identification possible without knowing the structure of the nonlinearity and the internal variable. The fundamental identifiability problem is solved and several schemes are presented.

The purpose of this paper is of twofold. First, we give a tutorial on a new approach to system identification using subband signal processing. Secondly, we study two types of subband identification schemes, one using critical sampling and one using over-sampling. We compare the behavior of the subband identification technique with the traditional "full-band" identification technique in terms of the computational cost, asymptotic residual error and convergence rate. This comparison is used to demonstrate the potential power of the subband technique. We also consider design issues for subband identification, especially for the case with over-sampling.

In this paper, we consider the problem of guaranteed cost control for a class of uncertain nonlinear systems. We derive LMI conditions for the regional robust stability and performance problem based on Lyapunov functions which are polynomial functions of the state and uncertain parameters. Based on the stability results, we discuss the synthesis problem for a class of affine control systems. Numerical examples are presented to illustrate our method.

In this paper, we study the problem of finite horizon Kalman filtering for systems involving a norm-bounded uncertain block. A new technique is presented for robust Kalman filter design. This technique involves using multiple scaling parameters which can be optimized by solving a semidefinite program. The use of optimized scaling parameters leads to an improved design. Also proposed is a recursive design method which can be applied to real-time applications.

Face recognition is an important research area with many potential applications such as biometric security. Among various techniques, eigenface method by principal component analysis (PCA) of face images has been widely used. In traditional eigenface methods, PCA was used to get the eigenvectors of the covariance matrix of a training set of face images and recognition was achieved by applying a template matching scheme with the vectors obtained by projecting new faces along a small number of eigenfaces. In order to avoid the time consuming step of recomputing eigenfaces when new faces are added, we use a set of modules to generate PCA based face representation for each subjects instead of PCA of entire face images. The localized nature of the representation makes the system easy to maintain and tolerant of local facial characteristic changes. Results indicate that the modular scheme yield accurate recognition on the widely used Olivetti Research Laboratory (ORL) face database.

In the general non-linear, non-Gaussian case, the Bayesian tracking formulas lack an analytic expression. For this reason a number of numerical approximate solutions are available. The most accurate solutions approximate the probability distributions (PDs) appearing in the Bayesian tracking recursions using weighted sums of elementary functions (e.g., Dirac impulses or Gaussian functions). This often leads to a large number of parameters needed to represent a PD in order to achieve a desired accuracy. This makes these approaches numerically complex as well as unsuitable for distributed applications where neighbor nodes need to exchange PD information. In order to tackle this limitation, we do the key observation that the large number of required parameters results from the fact that this kind of parameterization permit approximating any possible PD. However, the PDs appearing in a given Bayesian tracking problem can only belong to certain family of possible PDs induced by the problem. We propose a Bayesian tracking method exploiting this idea. We start by modeling the induced family as a manifold within the set of all possible PDs. We then build a coordinate system for this manifold, which permits representing each PD within the family using its coordinates along the manifold. We then represent the Bayesian tracking formulas as non-linear transformations of manifold coordinates representing PDs. In this sense, the proposed Bayesian tracking approach can be thought as the natural extension to the non-linear, non-Gaussian case of the Kalman filter, as the latter also uses a minimum set of coefficients (i.e., mean and correlation matrix) to represent each PD within the Gaussian family induced by a linear, Gaussian problem. We present a numerical experiment showing the massive reduction of parameters required to represent PDs in a benchmark example.

A typical cyber-physical system setup includes a local system sending measurements of its internal state to a remote state estimator. A form of attack consists of an eavesdropper observing this information exchange. Secrecy coding schemes have been recently proposed to achieve immunity to eavesdropping. The essential idea consists in coding the transmitting information in a way such that a single packet lost by the eavesdropper causes an irrecoverable error of its state estimation. Common limitations of the available methods are the assumptions that the local system can directly measure its internal state and that the system is unstable. In this work, we drop these assumptions and consider the general case in which measurements are noisy linear combinations of an inaccessible internal state and that the system is not necessarily unstable. To design the coding scheme, we introduce the concept of total secrecy, meaning that if the eavesdropper misses a packet that is available at the remote estimator, the former behaves as if no further packets were received. We derive a sufficient condition for total secrecy, as well as the code achieving this property. Also, for the case in which we cannot guarantee total secrecy, we address the problem of designing a code achieving maximum secrecy in some sense. We present numerical examples illustrating our claims.

We consider a partially observable optimal control model in which the system and observation noises are correlated, and the cost criterion is in the form of an exponential of an integral. A new minimum principle criterion is derived and applied to compute the explicit solution of linear exponential Gaussian optimisation problem with correlated noises.

This article studies the stability issue of networked switched systems (NSSs) under denial-of-service (DoS) attacks. To address this issue, the derived limitations imposed on both the frequency of DoS attacks on each subsystem and the upper limit of attack duration that each subsystem can tolerate are mode-dependent, which is more efficient and flexible than the current results for NSSs. Moreover, we reveal the relationship between the upper bound of the average maximum tolerable attack duration associated with the corresponding subsystem and the actual mode-dependent average dwell time. Furthermore, we identify that the total tolerable DoS attack duration as a percentage of the system runtime in this article can be higher than existing results. Finally, an example is given to demonstrate the effectiveness of our work.

In this tutorial paper, we explore the field of quantized feedback control, which has gained significant attention due to the growing prevalence of networked control systems. These systems require the transmission of feedback information, such as measurements and control signals, over digital networks, presenting novel challenges in estimation and control design. Our examination encompasses various topics, including the minimal information needed for effective feedback control, the design of quantizers, strategies for quantized control design and estimation, achieving consensus control with quantized data, and the pursuit of high-precision tracking using quantized measurements.

Network localization serves as a fundamental component for enabling various position based operations in multi-agent systems, facilitating tasks like target searching and formation control by providing accurate position information for all nodes in the network. Network localization focuses on the challenge of determining the positions of nodes within a network, relying on the known positions of anchor nodes and internode relative measurements. Over the past few decades, distributed network localization has garnered significant attention from researchers. This paper aims to provide a review of main results and advancements in the field of distributed network localization, with a particular focus on the perspective of graph Laplacian. Owning to its favorable characteristics, graph Laplacian unifies various network localization, even when dealing with diverse types of internode relative measurements, into a unified protocol framework, which can be constructed by a linear method and ensure the global convergence.

In this paper, we study the optimal control problem of a linear quadratic stochastic system where the randomness results from multiplicative noises. Especially, two controllers having access to different information are involved in the system. Different from most of the existing results which are based on the condition that the information of multiplicative noise is known during the design of optimal controllers, we focus on a more general case that the statistical information of the multiplicative noise is inaccessible. Under this setting, we propose a stochastic approximation algorithm to derive the solutions to algebraic Riccati equations (AREs) and obtain the optimal and stabilizing decentralized controllers.

In this article, we consider the discrete-time stochastic linear quadratic (LQ) optimal control with both initial and terminal constraints. The main contribution includes two aspects: one is to provide a necessary and sufficient condition for the exact reachability of stochastic systems; the other is to characterize the solvability condition of the constrained stochastic LQ optimal control problem based on the exact reachability of the stochastic systems and obtain the explicitly optimal controller. The key technique is to innovatively transform the stochastic system governed by a forward stochastic difference equation into one governed by a backward stochastic difference equation. This way, we are able to solve the forward and backward stochastic difference equations derived from the stochastic maximum principle.

This article addresses the problem of controlling a nonlinear plant subject to uniformly quantized measurements to have its output track and/or reject a family of signals produced by some external generator. First, conditions based on passivity and the theory of output regulation are devised to achieve convergence of the quantized error, namely, the difference between the quantized output and the (artificially) quantized reference. Then, further conditions on the reference are shown such that the actual output error achieves asymptotic convergence to zero.

This paper considers the rational expectations model with multiplicative noise and input delay, where the system dynamics rely on the conditional expectations of future states. The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model. In particular, we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case. The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

This article focuses on solving a finite-horizon nonlinear optimal control problem by using the Pontryagin's maximum principle. In practical applications, linearization is a common approach for solving nonlinear dynamical systems. However, it is not universally applicable due to various reasons, such as instability and low accuracy. In contrast to linearization, the inherent challenge in directly solving the above nonlinear optimal control problem lies in addressing the highly coupled nonlinear forward and backward differential equations. In order to address this problem, an equivalent relationship is established between these equations and a new optimization problem. By exploiting the inherent relationship between supervised learning and an optimization problem from the view of a dynamical system, a deep neural network framework is constructed for describing the new optimization problem. Furthermore, a numerical algorithm for optimal control, which is very powerful for a large variety of nonlinear dynamical systems, is implemented by training a deep residual network. Finally, the effectiveness of the algorithm is demonstrated by solving a trajectory tracking control problem for automatic guided vehicle. The obtained results reveal that the proposed control scheme can achieve high-precision tracking.

This article is concerned with linear quadratic regulation (LQR) and stabilization problems for discrete-time stochastic systems with multiple input channels and input delays. In comparison with single-input-channel problems, a key difficulty, induced by the different delays in different input channels, is that the information sets for multiple controllers are required to be asymmetric and coupled. A novel technique, referred to as orthogonal decomposition-reorganization, is proposed to conquer the coupling between channels. After the technique is used, a new method based on some refined decompositions is provided to solve the delayed forward-backward stochastic difference equations, which overcomes the asymmetry and amounts to finding the solvability condition of the underlying LQR problems. The complete solutions of the finite- and infinite-horizon LQR problems are given by newly developing Riccati-type equations. Also, a necessary and sufficient stabilizing condition is obtained for the system restricted by a performance index. Finally, the effectiveness of the results is evaluated by a numerical example.

This paper is concerned with near-optimal source search problem using a multiagent system in cluttered indoor environments. The goal of the problem is to maximize the detection probability within the minimum search time. We propose a two-stage strategy to achieve this goal. In the first stage, a greedy approach is used to define a set of grid cells with the aim of maximizing the detection probability. In the second stage, an iterative branch-And-bound procedure is used to design the search paths of all agents so that all grid cells are visited by one agent and the largest search path among all agents is minimized. Simulation results show that the proposed search algorithm has better performance in terms of exploration time compared to other existing methods.

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of non-standard forward¿backward stochastic differential equations (FBSDEs). By solving the FBSDEs, we design a set of decentralized strategies by virtue of two differential Riccati equations. Instead of the ¿-Nash equilibrium in classical mean-field games, the set of decentralized strategies is shown to be a Nash equilibrium. For the infinite-horizon problem, a simple condition is given for the solvability of the algebraic Riccati equation arising from consensus. Furthermore, the social optimal control problem is studied. Under a mild condition, the decentralized social optimal control and the corresponding social cost are given.

This paper studies the stability problem for networked control systems. A general result is presented to determine either global uniform boundedness (GUB), global asymptotic stability (GAS) or input-to-state stability (ISS), for interconnected nonlinear systems. This result checks stability in terms of a scalar called the network gain, hence we call the result the network gain theorem. The result generalizes the previously known matrix small-gain theorem and cyclic small-gain theorem for ISS. As in these results, our theorem does not assess the stability of a given networked system, but of a whole family of networked systems satisfying certain common assumption. An advantage of our stability condition is that it is not only sufficient, but also necessary, in the sense that, if not met, there exists an unstable networked system within that family. To complement our theoretical result, we propose a fully distributed algorithm to compute the network gain. We present simulation results to illustrate the proposed algorithm.

We investigate the linear quadratic Gaussian-Stackelberg game under a class of nested observation information patterns. The follower uses its observation data to design its strategy, whereas the leader implements its strategy using global observation data. We show that the solution requires solving a new type of forward-backward stochastic differential equation, whose drift components contain two conditional expectation terms associated with the adjoint variables. We then propose a method to find the functional relations between each adjoint pair, i.e., each pair formed by an adjoint variable and the conditional expectation of its associated state. The proposed method follows a layered pattern. More precisely, in the inner layer, we seek the functional relation for the adjoint pair under the sigma-subalgebra generated by follower's observation information, and in the outer layer, we look for the functional relation for the adjoint pair under the sigma-subalgebra generated by leader's observation information. Our result shows that the optimal open-loop solution admits an explicit feedback type representation.

In this paper, we present a Q-learning framework for solving finite-horizon zero-sum game problems involving the H8 control of linear system without knowing the dynamics. Research in the past mainly focused on solving problems in infinite horizon with completely measurable state. However, in the practical engineering, the system state is not always directly accessible, and it is difficult to solve the time-varying Riccati equation associated with the finite-horizon setting directly either. The main contribution of the proposed model-free algorithm is to determine the optimal output feedback policies without measurement state in finite-horizon setting. To achieve this goal, we first describe the Q-function caused by finite-horizon problems in the context of state feedback, then we parameterize the Q-functions as input¿output vectors functions. Finally, the numerical examples on aircraft dynamics demonstrate the algorithm's efficiency.

This paper introduces several related distributed algorithms, generalised from the celebrated belief propagation algorithm for statistical learning. These algorithms are suitable for a class of computational problems in large-scale networked systems, ranging from average consensus, sensor fusion, distributed estimation, distributed optimisation, distributed control, and distributed learning. By expressing the underlying computational problem as a sparse linear system, each algorithm operates at each node of the network graph and computes iteratively the desired solution. The behaviours of these algorithms are discussed in terms of the network graph topology and parameters of the corresponding computational problem. A number of examples are presented to illustrate their applications. Also introduced is a message-passing algorithm for distributed convex optimisation.

This letter explores the internal model principle in order to achieve asymptotic tracking of discrete-time systems subject to output quantization. It is shown that, by artificially quantizing the reference signal, asymptotic tracking can be achieved for a class of systems and references: discrete-time positive real systems, and persistent references in the form of sums of sinusoids. Given the importance of discrete time positive real functions, a systematic way of constructing them is also provided as a contribution. The resulting controller relies on frequency domain tools and may be designed by traditional linear techniques.

This paper studies the stability problem for networked control systems. A general result, called network gain theorem, is introduced to determine the input-to-state stability (ISS) for interconnected nonlinear systems. We show how this result generalises the previously known small gain theorem and cyclic small gain theorem for ISS. For the case of linear networked systems, a complete characterisation of the stability condition is provided, together with two distributed algorithms for computing the network gain: the classical Jacobi iterations and a message-passing algorithm. For the case of nonlinear networked systems, characterisation of the ISS condition can be done using M-functions, and Jacobi iterations can be used to compute the network gain.

This paper studies a linear-quadratic optimal control problem for discrete-time systems with multiplicative noise and random coefficients. Motivated by fiscal policy planning problems, where deterministic policies are required, this paper aims to find a deterministic optimal controller. The challenge is to seek a solution to forward and backward stochastic difference equations with structural inconsistency caused by random and deterministic terms. We derive necessary and sufficient conditions to solve this optimal control problem by employing a decoupling method. We also present an explicit expression of the optimal controller based on coupled stochastic Riccati-type difference equations.

In this paper, we investigate the optimal control strategies for model-free zero-sum games involving the (Figure presented.) control. The key contribution is the development of a Q-learning algorithm for linear quadratic games without knowing the system dynamics. The finite-horizon setting is more practical than the infinite-horizon setting, but it is difficult to solve the time-varying Riccati equation associated with the finite-horizon setting directly. The proposed algorithm is shown to solve the time-varying Riccati equation iteratively without the use of models, and numerical experiments on aircraft dynamics demonstrate the algorithm's efficiency.

This article proposes a novel control design method for high-precision positioning systems. The method aims to eliminate the tracking error caused by measurement quantization present in positioning systems with incremental encoders. By employing a combined internal model based feedback and quantized feedforward design, we are able to make the output of the positioning system asymptotically track any input signal with one or more sinusoidal components of known frequencies and a possible constant component. When combined with a micro-actuator, the resulting dual-stage positioning system is able to track any continuous periodic signal with a known period. Besides theoretical guarantees, the proposed design is validated experimentally and proved able to achieve asymptotic tracking error below ± 1 µ m when subject to a sensor quantization level of 5 µ m.

In this article, we study the feedback Nash strategy of the model-free nonzero-sum difference game. The main contribution is to present the Q -learning algorithm for the linear quadratic game without prior knowledge of the system model. It is noted that the studied game is in finite horizon which is novel to the learning algorithms in the literature which are mostly for the infinite-horizon Nash strategy. The key is to characterize the Q -factors in terms of the arbitrary control input and state information. A numerical example is given to verify the effectiveness of the proposed algorithm.

In this paper, we solve the stabilization problem of linear switched systems subject to external disturbances via an event-based state-dependent switching strategy. The proposed event-triggered switching rule can relax the conditions which guarantee the stability of switched systems so as to attain more feasible solutions than the previous work. As a result, a better bound of L2 gain performance of the system is obtained over the set of admissible disturbances. The elimination of Zeno behavior for state-dependent switched system is also proven. Finally, numerical simulations illustrate the validity of the proposed theoretical results.

This paper studies the convergence properties of a recently proposed distributed algorithm for weighted least-squares (WLS) estimation in networked systems. This algorithm is suitable for large-scale networks with a vector parameter (variable) in each node of the network. By establishing the connection between this algorithm and the celebrated Gaussian Belief Propagation (BP) algorithm for statistical learning with scalar variables, asymptotic convergence of the algorithm is established under the assumption of generalised block diagonal dominance. This result generalises the known asymptotic convergence result of the Gaussian BP algorithm for networks with scalar variables. By extending the notion of diagonal dominance to block matrices, we are able to generalise the so-called walk-sum approach for convergence analysis of the Gaussian BP algorithm to this distributed WLS algorithm and show a similar asymptotic convergence property for networks with vector parameters. The significance of our work is that it gives theoretical guarantee for the distributed WLS algorithm for a new class of large-scale networked systems with vector parameters.

The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the sum of local functions known at individual nodes. A number of methods, having different advantages, are available for addressing this problem. The goal of this article is to achieve the maximum possible convergence rate. As the first step toward this end, we propose a new method, which we show converges faster than other available options. As the second step toward our goal, we complement the proposed method with a fully distributed method for estimating the optimal step size that maximizes the convergence rate. We provide theoretical guarantees for the convergence of the resulting method in a neighborhood of the solution. We present numerical experiments showing that, when using the same step size, our method converges significantly faster than its rivals. Experiments also show that the distributed step-size estimation method achieves an asymptotic convergence rate very close to the theoretical maximum.

We study the problem of detecting an attack on a stochastic cyber-physical system. We aim to treat the problem in its most general form. We start by introducing the notion of asymptotically detectable attacks, as those attacks introducing changes to the system's output statistics which persist asymptotically. We then provide a necessary and sufficient condition for asymptotic detectability. This condition preserves generality as it holds under no restrictive assumption on the system and attacking scheme. To show the importance of this condition, we apply it to detect certain attacking schemes which are undetectable using simple statistics. Our necessary and sufficient condition naturally leads to an algorithm which gives a confidence level for attack detection. We present simulation results to illustrate the performance of this algorithm.

In this article, we study the impact of stealthy attacks on the cyber-physical system (CPS) modeled as a stochastic linear system. An attack is characterised by a malicious injection into the system through input, output or both, and it is called stealthy (resp. strictly stealthy) if it produces bounded changes (resp. no changes) in the detection residue. Correspondingly, a CPS is called vulnerable (resp. strictly vulnerable) if it can be destabilized by a stealthy attack (resp. strictly stealthy attack). We provide necessary and sufficient conditions for the vulnerability and strictly vulnerability. For the invulnerable case, we also provide a performance bound for the difference between healthy and attacked system. Numerical examples are provided to illustrate the theoretical results.

A popular approach for solving the indoor dynamic localization problem based on WiFi measurements consists of using particle filtering. However, a drawback of this approach is that a very large number of particles are needed to achieve accurate results in real environments. The reason for this drawback is that, in this particular application, classical particle filtering wastes many unnecessary particles. To remedy this, we propose a novel particle filtering method which we call maximum likelihood particle filter (MLPF). The essential idea consists of combining the particle prediction and update steps into a single one in which all particles are efficiently used. This drastically reduces the number of particles, leading to numerically feasible algorithms with high accuracy. We provide experimental results, using real data, confirming our claim.

In this article we study the problem of localizing a fleet of vehicles in an indoor environment using ultra-wideband (UWB) signals. This is typically done by placing a number of UWB anchors with respect to which vehicles measure their distances. The localization performance is usually poor in the vertical axis, due to the fact that anchors are often placed at similar heights. To improve accuracy, we study the use of inter-vehicle distance measurements. These measurements introduce a technical challenge, as this requires the joint estimation of positions of all vehicles, and currently available methods become numerically complex. To go around this, we use a recently proposed technique called maximum likelihood Kalman filtering (MLKF). We present experiments using real data, showing how the addition of inter-vehicle measurements improves the localization accuracy by about 60%. Experiments also show that the MLKF achieves a localization error similar to the best among available methods, while requiring only about 20% of computational time.

This paper studies the convergence properties of the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple bound for the convergence rate is provided for message-passing. In comparison with previous results, our results do not require the given convex program to have known convex pairwise components and that our bound for the convergence rate is tighter and simpler. When specialised to quadratic optimisation, we generalise known results by providing a very simple bound for the convergence rate.

This paper examines the finite horizon optimal control problem and infinite horizon stabilization problem for Markov jump linear system (MJLS) with input delay. The essential obstacle encountered in this paper is that the optimal controller cannot be represented as a product of a deterministic gain and a state predictor. This paper presents a complete solution to the problems: (1) For the finite horizon, the necessary and sufficient solvability condition of the optimal control and the analytical controller are given based on the modified coupled difference Riccati equation defined herein. (2) For the infinite horizon, the necessary and sufficient stabilization conditions are explored under explicit expressions, and the optimal controller is designed with a modified coupled algebraic Riccati equation (CARE). We show that under the exact observability assumption, the MJLS with input delay is stabilizable in the mean-square sense with the optimal controller if and only if the CARE has a particular positive definite solution. The introduction of a delayed forward and backward Markov difference equation and the definition of a new type of Lyapunov function form the basic tools to solving this problem.

We study a distributed Kalman filtering problem in which a number of nodes cooperate without central coordination to estimate a common state based on local measurements and data received from neighbors. This is typically done by running a local filter at each node using information obtained through some procedure for fusing data across the network. A common problem with existing methods is that the outcome of local filters at each time step depends on the data fused at the previous step. We propose an alternative approach to eliminate this error propagation. The proposed local filters are guaranteed to be stable under some mild conditions on certain global structural data, and their fusion yields the centralized Kalman estimate. The main feature of the new approach is that fusion errors introduced at a given time step do not carry over to subsequent steps. This offers advantages in many situations including when a global estimate is only needed at a rate slower than that of measurements or when there are network interruptions. If the global structural data can be fused correctly asymptotically, the stability of local filters is equivalent to that of the centralized Kalman filter. Otherwise, we provide conditions to guarantee stability and bound the resulting estimation error. Numerical experiments are given to show the advantage of our method over other existing alternatives.

This paper proposes fast convergent distributed algorithms for weighted average consensus of input data. For acyclic graphs, we give an algorithm that converges to the exact weighted average consensus in a finite number of iterations, equal to the graph diameter. For loopy (cyclic) graphs, we offer two remedies. In the first one, we give another distributed algorithm to enable our average consensus algorithm applicable to a loopy graph by converting it into a spanning tree. In the second one, we consider a slightly modified average consensus problem whose optimal solution approximates the consensus solution with arbitrary precision, and give a modified average consensus algorithm with guaranteed exponential convergence to the optimal solution. The proposed average consensus algorithms enjoy low complexities, robustness to transmission adversaries, and asynchronous implementation. Our algorithms are conceptually different from the popular graph Laplacian approach, and converge much faster than the latter approach.

This article proposes a macro-micro approach to deal with sensor quantization in positioning systems. First, a control strategy able to asymptotically drive the quantized (macro) actuator toward an oscillatory motion around the desired reference is presented. A microactuator is, then, added to compensate for these oscillations so that the reference is asymptotically tracked. Besides theoretical guarantees, the proposed strategy is validated in an experimental setup and proved able to achieve a steady-state tracking error within $\pm 0.2~\mu \text{m}$ when subject to a sensor quantization level of $5~\mu \text{m}$. Perfect knowledge of the system parameters is not necessary to design and implement the proposed control strategy, which relies on the internal model principle and makes use of traditional frequency domain tools.

This paper investigates the linear quadratic Gaussian Stackelberg game under asymmetric information. Two decision makers implement control strategies using different information patterns: The follower uses its observation information to design its strategy, whereas the leader implements its strategy using global information. For this problem, the separation principle becomes invalid. Instead, we apply the classical variation method to derive conditions to be satisfied by both decision makers. We show that the solution attributes to solving a two-point boundary value problem of stochastic version whose drift terms contain some conditional mean terms. We then propose a layered calculation method to solve this problem. In the inner layer calculation, the adjoint state variable's estimate is expressed as a linear functional of the state estimate. In the outer layer calculation, the adjoint state variable is expressed as a linear functional of the state and its estimate. We also verify that the Kalman¿Bucy filter works for computing the state estimate. The result is also applied to dynamic duopoly with sticky prices and pursuit¿evasion problem.

We propose a distributed method for tracking a target with linear dynamics and non-linear measurements acquired by a number of sensors. The proposed method is based on a Bayesian tracking technique called maximum likelihood Kalman filter (MLKF), which is known to be asymptotically optimal, in the mean squared sense, as the number of sensors becomes large. This method requires, at each time step, the solution of a maximum likelihood (ML) estimation problem as well as the Hessian matrix of the likelihood function at the optimal. In order to obtain a distributed method, we compute the ML estimate using a recently proposed fully distributed optimization method, which yields the required Hessian matrix as a byproduct of the optimization procedure. We call the algorithm so obtained the distributed MLKF (DMLKF). Numerical simulation results show that DMLKF largely outperforms other available distributed tracking methods, in terms of tracking accuracy, and that it asymptotically approximates the optimal Bayesian tracking solution, as the number of sensors and inter-node information fusion iterations increase.

This article focuses on the distributed static estimation problem. A belief propagation (BP) based estimation algorithm is studied for its convergence and accuracy. More precisely, we give conditions under which the BP-based distributed estimator is guaranteed to converge and we give concrete characterizations for its accuracy. Our results reveal new insights and properties of this distributed algorithm, leading to better theoretical understanding of static distributed state estimation and new applications of the algorithm.

This article proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalized diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on local information exchange between neighboring nodes, local computation, and local storage. For an acyclic graph under the condition of diagonal dominance, the algorithm is shown to converge to the correct solution in a finite number of iterations, equaling the graph diameter. For a loopy graph, the algorithm is shown to converge to the correct solution asymptotically. Simulations verify that the proposed algorithm significantly outperforms the classical Jacobi method and an orthogonal projection-based method.

This paper studies the problem of distributed weighted least-squares (WLS) estimation for an interconnected linear measurement network with additive noise. Two types of measurements are considered: self measurements for individual nodes, and edge measurements for the connecting nodes. Each node in the network carries out distributed estimation by using its own measurement and information transmitted from its neighbours. We study two distributed estimation algorithms: a recently proposed distributed WLS algorithm and the so-called Gaussian Belief Propagation (BP) algorithm. We first establish the equivalence of the two algorithms. We then prove a key result which shows that the information matrix is always generalized diagonally dominant, under some very mild condition. Using these two results and some known convergence properties of the Gaussian BP algorithm, we show that the aforementioned distributed WLS algorithm computes the exact WLS solution asymptotically. A bound on its convergence rate is also presented.

In traditional adaptive control, the certainty equivalence principle suggests a two-step design scheme. A controller is first designed for the ideal situation assuming the uncertain parameter was known, and it renders a Lyapunov function. Then, the uncertain parameter in the controller is replaced by its estimation that is updated by an adaptive law along the gradient of Lyapunov function. This principle does not generally work for a multiagent system as an adaptive law based on the gradient of (centrally constructed) Lyapunov function cannot be implemented in a distributed fashion, except for limited situations. In this paper, we propose a novel distributed adaptive scheme, not relying on gradient of Lyapunov function, for general multiagent systems. In this scheme, asymptotic consensus of a second-order uncertain multiagent system is achieved in a network of directed graph.

This paper proposes a novel clock synchronization algorithm for wireless sensor networks (WSNs). The algorithm is derived using a fast finite-time average consensus idea, and is fully distributed, meaning that each node relies only on its local clock readings and reading announcements from its neighbours. For networks with an acyclic graph, the algorithm converges in only d iterations for clock rate synchronization and another d iterations for clock offset synchronization, where d is the graph diameter. The algorithm enjoys low computational and communicational complexities and robustness against transmission adversaries. Each node can execute the algorithm asynchronously without the need for global coordination. Due to its fast convergence, the algorithm is most suitable for large-scale WSNs. For WSNs with a cyclic graph, a fast distributed depth-first-search (DFS) algorithm can be applied first to form a spanning tree before applying the proposed synchronization algorithm.

In this study, consensus problem for general high-order multi-agent systems with communication delay is investigated. Given the unstable agent dynamics and a known communication delay, two consensus protocols are designed to guarantee consensus over undirected network. By jointly researching the effects of agent dynamics and network topology, allowable delay bounds depending on the maxima of concave functions are easy to calculate. Especially, the maximum delay bound is derived when the network topology is completely connected. The main approach for the same involves designing the control gains on the basis of the solution of a parametric algebraic Riccati equation. Finally, the theoretical results are demonstrated via numerical simulations.

This paper concentrates on coordinate-free formation control for directed networks, for which the dynamic motion of each agent is assumed to be governed only by a local control. We develop a graph Laplacian approach to solve the global and exponential formation stablization problem using merely relative position measurements between neighbors. First, to capture the sensing and control architectures that are needed to maintain the shape of a formation, a necessary and sufficient topological condition is proposed. Second, a Laplacian-based control law is developed for the stablization problem of a group of mobile agents to a desired formation shape under both fixed and switching topologies due to temporal node failures. Simulation results are provided to demonstrate that our Laplacian-based formation control strategy is inherently fault-tolerant and robust to node failures.

This paper studies a distributed state estimation problem for a network of linear dynamic systems (called nodes), which evolve autonomously, but their measurements are coupled through neighborhood interactions. Power networks are typical networked systems obeying such features, with other examples including traffic networks, sensor networks and many multi-agent systems. We develop a new distributed state estimation approach, for each node to update its local state. The core of this distributed approach is a distributed maximum a posteriori (MAP) estimation technique, which delivers a globally optimal estimate under certain assumptions. We apply the distributed approach to an IEEE 118-bus system, and compare it with a centralized approach, which provides the optimal state estimate using all the measurements, and with a local state estimation approach, which uses only local measurements to estimate local states. Simulation results show that under different scenarios including normal operation, bad measurements and sudden load change, the distributed approach is clearly more accurate than the local state estimation approach and distributed static state estimation approach. Although the result is a bit less accurate than that by a centralized algorithm, the distributed algorithm enjoys low computational complexity and communication load, and is scalable to large power networks.

This paper studies the consensusability of a continuous-time linear time-invariant multi-agent system (MAS) with time delay in an undirected network with N nodes. We show that the MAS can achieve consensus if and only if N - 1 time-delay subsystems associated with the eigenvalues of the Laplacian matrix of the network are simultaneously asymptotically stable. By employing a linear matrix inequality (LMI) method, we present a controller design method for a MAS to reach consensus. We also obtain a bound on the maximum time delay for consensusability for a MAS with first-order integrator dynamics by using frequency-domain analysis. Copyright © 2015 John Wiley & Sons, Ltd.

This paper considers the collaborative localization problem for a team of mobile agents. The goal is to estimate the relative coordinate of each agent with respect to a stationary landmark. Each agent is supposed to be able to measure its own velocity and the distances to nearby agents as well as the change rates of the distances. Due to limited sensing capability, movements of agents and possible interference of severe environments, the topology describing the measurements and communication information flow among the agents and the landmark is usually time-varying. Under such a scenario, this paper develops a consensus-like fusion scheme together with a continuous-time estimator for the collaborative localization problem. It is proved that the fused estimate of each agent's position globally asymptotically converges to its true value if the movements of the agents satisfy a persistent excitation condition and each agent is uniformly jointly reachable from the landmark in the time-varying topology. The effectiveness of the proposed scheme is verified through simulations without and with measurement noises.

This paper introduces a new multi-agent control problem, called an affine formation control problem, with the objective of asymptotically reaching a configuration that preserves collinearity and ratios of distances with respect to a target configuration. Suppose each agent updates its own state using a weighted sum of its neighbor's relative states with possibly negative weights. Then the affine control problemcan be solved for either undirected or directed interaction graphs. It is shown in this paper that an affine formation is stabilizable over an undirected graph if and only if the undirected graph is universally rigid,while an affine formation is stabilizable over a directed graph in the d-dimensional space if and only if the directed graph is (d + 1)-rooted. Rigorous analysis is provided, mainly relying on Laplacian associated with the interaction graph, which contain both positive and negative weights.

This paper focuses on the procurement of load shifting service by optimally scheduling the charging and discharging of PEVs in a decentralized fashion. We assume that the energy flow between PEVs and the grid is bidirectional, i.e., PEVs can also release energy back into the grid as distributed generation, which is known as vehicle-to-grid (V2G). The optimal scheduling problem is then formulated as a mixed discrete programming (MDP) problem, which is NP-hard and extremely difficult to solve directly. To get over this difficulty, we propose a solvable approximation of the MDP problem by exploiting the shape feature of the base demand curve during the night, and develop a decentralized algorithm based on iterative water-filling. Our algorithm is decentralized in the sense that the PEVs compute locally and communicate with an aggregator. The advantages of our algorithm include reduction in computational burden and privacy preserving. Simulation results are given to show the performance of our algorithm.

The paper studies the general circumnavigation problem for a team of unicycle-type agents, with the goal of achieving specific circular formations and circling on different orbits centered at a target of interest. A novel distributed solution is proposed, in which the control laws are heterogeneous for the agents such that some agents are repellant from the target while attractive to its unique neighbor and some agents are attractive to the target while repellant from its neighbor. A systematic procedure is developed to design the control parameters according to the specific radii of the orbits and the formations that the agents are desired to converge to. Moreover, this control scheme uses a minimum number of information flow links between the agents and local measurements of relative position only. Based on the block diagonalization of circulant matrices by a Fourier transform, asymptotic convergence properties are analyzed rigorously. The validity of the proposed control algorithm is also demonstrated through numerical simulations.

This paper studies the state estimation problem for a stochastic discrete-time system over a lossy channel where the packet loss is modeled as an independent and identically distributed binary process. To counter the effect of random packet loss, we propose a linear coding method to preprocess the measured output, and prove that the coded output is information preserving when packet loss is void and is information enhancing when packet loss is present. An optimal state estimator under the minimum mean square error (MMSE) criterion is derived for the coded output when subject to packet loss. The maximum packet loss rate for ensuring a stable estimator is then derived and shown to be very close to a well-known lower bound. Also considered is a compressed linear coding method where the measured output is first compressed onto a lower dimensional space before encoding, and it is shown that the similar packet rate condition for stability holds.

This paper studies a networked state estimation problem for a spatially large linear system with a distributed array of sensors, each of which offers partial state measurements. A lossy communication network is used to transmit the sensor measurements to a central estimator where the minimum mean square error (MMSE) state estimate is computed. Under a Markovian packet loss model, we provide necessary and sufficient conditions for the stability of the estimator for any diagonalizable system in the sense that the mean of the state estimation error covariance matrix is uniformly bounded. In particular, the stability conditions for the second-order systems with an i.i.d. packet loss model are explicitly expressed as simple inequalities in terms of the largest open-loop pole and the packet loss rate.

In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods.

In this paper, we study the mean square stability of Kalman filtering of a discrete-time stochastic system under two periodically switching sensors. The sensor measurements are sent to a remote estimator over a lossy channel whose packet loss process is independent and identically distributed. We prove that the problem can be converted into the stability analysis of Kalman filtering using two sensors at each time, and the measurements of each sensor are transmitted to the estimator via an independent lossy channel of the same packet loss rate. Some necessary and/or sufficient conditions for stability of the estimation error covariance matrices are derived. Moreover, the effect of the sensor switching on the filter stability is revealed. Their implications and relationships with related results in the literature are discussed.

This paper investigates the LQG control problem for networked control systems (NCSs) with packet losses, where the packet losses are considered to appear in both the sensor-to-controller channel and controller-to-actuator channel. Bernoulli random processes are used to describe the packet losses in the two channels. Two simple compensation schemes are explored for state estimation with missing measurements in which the input of the plant is set to zero if a packet is lost, and the hold-input strategy, in which the previous input is used with packet dropout. The optimal static controller gains and the critical loss probabilities for the two schemes are presented, and their performances are compared in terms of numerical simulations. The conclusion is that neither of the two schemes can be claimed to be superior to the other, as the stability regions of the two strategies are reversely complemented to each other whether for the scalar or vector example.