Professor Minyue Fu

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.

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.

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.

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.

The category, direction identification and positioning of polar electronic components play an important role in the industrial production, welding and inspection. In this paper, we first successfully transform the original problem of directional identification of polar electronic components into a classification problem. Then, the Faster RCNN (region convolutional neural network) and YOLOv3 methods are used to realize the correct classification, direction identification and accurate positioning of the polar electronic components. The experiments validate the effectiveness of our proposed method and the mAP (mean average precision) of the two proposed algorithms can reach 97.05 %, 99.22 %. In addition, we improve the anchor boxes of the Faster RCNN and YOLOv3 by K-means algorithm through the length and width distributions of the target frames of the datasets, the accuracy can be improved by 1.16 %, 0.1 %. We also propose the YOLOv3-BigObject network structure for the large target detection, while improving the accuracy, the cost time for detecting a single picture is also greatly reduced. Finally, the board with the electronic components is chosen to test and good experimental results are obtained.

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.

This paper proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalised diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on local information exchange between neighbouring 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, equalling 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 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.

This paper concentrates on the formation merging control problem for a leader-follower network. The objective is to control a team of agents called followers such that they are merged with another team of agents called leaders to form a single globally rigid formation. A method based on graph Laplacian is introduced to address this problem. Each follower selects its interaction neighbors and interaction weights according to the given target configuration. The graph modeling the interaction topology of all the agents is directed and time-varying. First, by assuming that the synchronized velocity of the leaders is known to all the followers, a necessary and sufficient condition is derived to ensure uniform asymptotic formation merging. Second, we relax this assumption and consider that the velocity of the leaders is known to only a subset of followers, for which the same necessary and sufficient condition is obtained with the help of an internal model for velocity synchronization.

This paper studies the 2D localization problem of a sensor network given anchor node positions in a common global coordinate frame and relative position measurements in local coordinate frames between node pairs. It is assumed that the local coordinate frames of different sensors have different orientations and the orientation difference with respect to the global coordinate frame are not known. In terms of graph connectivity, a necessary and sufficient condition is obtained for self-localizability that leads to a fully distributed localization algorithm. Moreover, a distributed verification algorithm is developed to check the graph connectivity condition, which can terminate successfully when the sensor network is self-localizable. Finally, a fully distributed, linear, and iterative algorithm based on the complex-valued Laplacian associated with the sensor network is proposed, which converges globally and gives the correct localization result.

Bayesian tracking is a general technique for state estimation of nonlinear dynamic systems, but it suffers from the drawback of computational complexity. This paper is concerned with a class of Wiener systems with multiple nonlinear sensors. Such a system consists of a linear dynamic system followed by a set of static nonlinear measurements. We study a maximum-likelihood Kalman filtering (MLKF) technique which involves maximum-likelihood estimation of the nonlinear measurements followed by classical Kalman filtering. This technique permits a distributed implementation of the Bayesian tracker and guarantees the boundedness of the estimation error. The focus of this paper is to study the extent to which the MLKF technique approximates the theoretically optimal Bayesian tracker. We provide conditions to guarantee that this approximation becomes asymptotically exact as the number of sensors becomes large. Two case studies are analyzed in detail.

Plug-in hybrid electric vehicles (PHEV) are expected to become widespread in the near future. However, high penetration of PHEVs can overload the distribution system. In smart grid, the charging of PHEVs can be controlled to reduce the peak load, known as demand-side management (DSM). In this paper, we focus on the DSM for PHEV charging at low-voltage transformers (LVTs). The objective is to flatten the load curve of LVTs, while satisfying each consumer's requirement for their PHEV to be charged to the required level by the specified time. We first formulate this problem as a convex optimization problem and then propose a decentralized water-filling-based algorithm to solve it. A moving horizon approach is utilized to handle the random arrival of PHEVs and the inaccuracy of the forecast nonPHEV load. We focus on decentralized solutions so that computational load can be shared by individual PHEV chargers and the algorithm is scalable. Numerical simulations are given to demonstrate the effectiveness of our algorithm.

This study studies a sensor scheduling problem for the state estimation of a stochastic discrete-time system where the measurements are to be sent from multiple sensors to a centralised estimator through a lossy channel. By adopting a carrier sense multiple access/collision avoidance (CSMA/CA) protocol, the packet loss rate of the channel increases with the number of competing sensors for data communication. To increase the channel utilisation, it requires to smartly select informative sensors to transmit their measurements. Depending on the availability of the acknowledgment (ACK) messages from the estimator, both online and offline algorithms for scheduling sensor communication are proposed to optimise the expected performance of minimum mean-square error state estimator. Particularly, the online scheduling uses the ACK to trigger the sensor communication while the offline version adopts a random transmission framework and only decides the probability of sending measurements for each sensor in an offline manner. The optimal online scheduler is given by the solution of an integer programming, which is approximated by a practically solvable optimisation. Simulations are included to demonstrate the effectiveness of the proposed algorithms.

This paper addresses the stability of a Kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator. We give a necessary condition and a sufficient condition, with a trivial gap between them, for the boundedness of the expected value of the estimation error covariance. These conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order Markov process. Hence, we extend the class of systems for which these conditions are known in two directions, namely, by including degenerate systems, and by considering network models more general than i.i.d. and Gilbert-Elliott. We show that these conditions recover known results from the literature when evaluated for non-degenerate systems under the assumption of i.i.d. or Gilbert-Elliott packet loss models.

This paper studies the problem of determining the sensor locations in a large sensor network using only relative distance (range) measurements. Based on a generalized barycentric coordinate representation, our work generalizes the DILOC algorithm to the localization problem under arbitrary deployments of sensor nodes and anchor nodes. First, a criterion and algorithm are developed to determine a generalized barycentric coordinate of a node with respect to its neighboring nodes, which do not require the node to be inside the convex hull of its neighbors. Next, for the localization problem based on the generalized barycentric coordinate representation, a necessary and sufficient condition for the localizability of a sensor network with a generic configuration is obtained. Finally, a new linear iterative algorithm is proposed to ensure distributed implementation as well as global convergence to the true coordinates. © 2014 IEEE.

The state estimation problem is studied for the networked control systems subject to random communication delays and the measurements without time stamps. With the random delay bounded by one step only, a new measurement model is proposed for possibly out-of-sequence measurements. For unstable systems, to guarantee that the estimator is linear unbiased and the estimation error covariance is uniformly bounded, we show that the estimator structure is given based on the average of all received measurements at each time. The estimator gains can be derived by solving a set of recursive discrete-time Riccati equations. The estimator is guaranteed to be optimal in the sense that it is unbiased with uniformly bounded estimation error covariance. A simulation example shows the effectiveness of the proposed algorithm. Copyright © 2013 Acta Automatica Sinica.

This paper is concerned with optimal filter problems for networked systems with random transmission delays, while the delay process is modeled as a multi-state Markov chain. By defining a delay-free observation sequence, the optimal filter problems are transformed into ones of the Markov jumping parameter system. We first present an optimal Kalman filter, which is with time-varying, path-dependent filter gains, and the number of the paths grows exponentially in time delay. Thus an alternative optimal Markov jump linear filter is presented, in which the filter gains just depend on the present value of the Markov chain. Further, an optimal filter with constant-gains is developed, the existence condition for the stabilizing solutions to the filter is given, and it can be shown that the proposed Markov jump linear filter converges to the constant-gain filter under appropriate assumptions. © 2013 Elsevier Ltd. All rights reserved.

Walsh filtering has been used as a method to reduce receiver complexity in several coding and modulation systems, especially in continuous phase modulation systems. In this paper, we show that its lowpass filtering ability is poor and alias components arising from an adjacent channel can significantly degrade the maximum-likelihood decoding. Instead, a lowpass filtering method is more robust against adjacent channel interference and thus gives less decoding errors than the Walsh filtering method. © 2004 IEEE.

In this paper, we study the validity of the separation principle for linear quadratic control of linear systems in the presence of control input saturation. Our result shows that the well-known separation principle for linear systems fails to hold in this case.

In this paper we study a probabilistic approach which is an alternative to the classical worst-case algorithms for robustness analysis and design of uncertain control systems. That is, we aim to estimate the probability that a control system with uncertain parameters q restricted to a box Q attains a given level of performance ¿. Since this probability depends on the underlying distribution, we address the following question: What is a "reasonable" distribution so that the estimated probability makes sense? To answer this question, we define two worst-case criteria and prove that the uniform distribution is optimal in both cases. In the second part of the paper we turn our attention to a subsequent problem. That is, we estimate the sizes of both the so-called "good" and "bad" sets via sampling. Roughly speaking, the good set contains the parameters q ¿ Q with a performance level better than or equal to ¿ while the bad set is the set of parameters q ¿ Q with a performance level worse than ¿. We give bounds on the minimum sample size to attain a good estimate of these sets in a certain probabilistic sense.

We consider the relative stability of time-invariant and time-varying unnormalized lattice filters. First, we consider a set of lattice filters whose reflection parameters a; obey a; 5; and provide necessary and sufficient conditions on the 5; that guarantee that each time-invariant lattice in the set has poles inside a circle of prescribed radius l/p 1, i.e., is relatively stable with degree of stability In p. We also show that the relative stability of the whole family is equivalent to the relative stability of a single filter obtained by fixing each a; to Si and can be checked with only the real poles of this filter. Counterexamples are given to show that a number of properties that hold for stability of LTI Lattices do not apply to relative stability verification. Second, we give a diagonal Lyapunov matrix that is useful in checking the above pole condition. Finally, we consider the time-varying problem where the reflection coefficients vary in a region where the frozen transfer functions have poles with magnitude less than l/p and provide bounds on their rate of variations that ensure that the zero input state solution of the time-varying lattice decays exponentially at a rate faster than I/pi > I/p. © 1998 IEEE.

We consider the relative stability of time-invariant and time-varying unnormalized lattice filters. First, we consider a set of lattice filters whose reflection parameters ai obey |ai| = di and provide necessary and sufficient conditions on the di that guarantee that each time-invariant lattice in the set has poles inside a circle of prescribed radius 1/¿ < 1, i.e., is relatively stable with degree of stability 1n ¿. We also show that the relative stability of the whole family is equivalent to the relative stability of a single filter obtained by fixing each ai to di and can be checked with only the real poles of this filter. Counterexamples are given to show that a number of properties that hold for stability of LTI Lattices do not apply to relative stability verification. Second, we give a diagonal Lyapunov matrix that is useful in checking the above pole condition. Finally, we consider the time-varying problem where the reflection coefficients vary in a region where the frozen transfer functions have poles with magnitude less than 1/¿ and provide bounds on their rate of variations that ensure that the zero input state solution of the time-varying lattice decays exponentially at a rate faster than 1/¿1 > 1/¿.

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.