Emeritus Professor Rick Middleton

Cytosolic calcium ion levels are critical in sustaining neuronal activity. They have an intricate relationship with the neuronal energy systems, and Parkinson's disease (PD) probably involves a dysfunctional energy system in the pacemaking neurons of the Substantia nigra. This chapter explores the association of repetitive firing pattern of these neurons and cytosolic calcium using a mathemat-ical model. In particular, a theory is examined that proposes a role of low voltage activated L-type calcium channel in creating an energy stress within vulnerable neurons.

It is well known that feedback may be used in a control design to obtain desirable properties that are not achievable with open-loop control. Among these are the ability to stabilize an unstable system and "73648_C010" - #2 to reduce the effects of plant disturbances and modeling errors upon the system output. On the other hand, use of feedback control can also have undesirable consequences: feedback may destabilize a system, introducemeasurement noise, amplify the effects of disturbances andmodeling errors, and generate large control signals. A satisfactory control design will, if possible, achieve the potential benefits of feedback without incurring excessive costs.

In this paper, a switched controller for the Chaplygin Sleigh system based on passivity and energy shaping is presented. The Chaplygin sleigh cannot be asymptotically stabilised with a smooth control law, since Brockett's necessary conditions for smooth stabilisation is not satisfied. To asymptotically stabilise the origin, two potential energy shaping control laws are developed that render the system asymptotically stable to two equilibrium manifolds, which intersect at the origin. A switching strategy between the energy shaping controllers is derived that ensures the system converges to the intersection of the equilibrium manifolds.

In this paper, a consensus problem is studied for a group of second-order nonlinear heterogeneous agents with uniform time delay in communication links and uncertainty in agent dynamics. We design a class of novel decentralized control protocols for the consensus problem whose solvability is converted into stability analysis of an associated closed-loop system with uncertainty and time delay. Using an explicitly constructed Lyapunov functional, stability conditions and solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities (LMIs) apart from a small number of scalar parameters that appear nonlinearly. The effectiveness of the proposed control protocol is illustrated by numerical examples.

Recently the additive increase multiplicative decrease (AIMD) algorithm has been applied in fields other than congestion control in communications networks. A major attribute of these new applications is that the share of each user is bounded. Simulations suggest that AIMD performs well, even in the case of individual constraints on each user. In this paper, we provide a formal proof of exponential convergence to a unique fixed-point for the AIMD algorithm under individual user constraints.

The additive increase multiplicative decrease (AIMD) algorithm, that is commonly used for congestion avoidance in communication networks, has recently been suggested in other fields such as load management in electric power networks. As for congestion avoidance, in such systems a large number of agents are required to share a given resource. In recent work by Shorten, Wirth and Leith on congestion control in networking a stochastic model has been developed to analyse AIMD algorithms. However, the analysis assumes a continuous implementation of the algorithm and a constant available resource. These assumptions are no longer useful if the AIMD algorithm is applied in fields such as load management in electric power networks, where a discrete implementation is often required, and the available resource shared may be inherently variable. In this paper we develop a disturbed AIMD model based on the model introduced by Shorten et al. that includes discrete time implementation and time varying resource availability. Further, we use that model to bound the influence of these disturbances, caused by either a discrete implementation or small variations in the available resource.

This paper addresses the problem of designing static feedback controllers for 2D mixed continuous-discrete-time systems via linear matrix inequalities (LMIs). It is shown that a necessary and sufficient condition can be obtained by solving two LMI problems. The first LMI problem aims at determining a polynomial whose positivity domain corresponds to stabilizing controllers. The second LMI problem aims at identifying one controller in such a domain. The condition is sufficient for any size of the LMI problems, and is necessary for a sufficiently large one. Some numerical examples illustrate the proposed methodology.

This paper presents the properties of a new variant of model predictive control called Reduced Parameterisation Model Predictive Control (RPMPC). The new algorithm uses the structure of the null controllable set of input constrained unstable systems to produce a closed-loop system with a region of attraction that is an arbitrarily close approximation to this set. We show that the RPMPC algorithm converges in a finite number of iterations and we establish stability of the resulting closed-loop system. In addition, we present a rigorous worst case complexity analysis together with average computational tests. Both these studies show that for long horizons RPMPC has a lower computational requirement than that of standard MPC.

This paper introduces a new variant of model predictive control called Reduced Parameterisation Model Predictive Control. The new algorithm uses the structure of the null controllable set of input constrained unstable systems to produce a closed-loop system with a region of attraction that is an arbitrarily close approximation to this set. In addition, this result is achieved with a lower complexity than that of MPC.

Model Predictive Control (MPC) is a popular advanced control strategy that is implemented by determining an optimal control sequence at each time step. One of the major contributors to MPC's computational complexity is the length of the control sequence or, equivalently, the number of optimisation parameters. This paper analyses the null controllable sets, and their related finite horizon approximation, of a class of unstable systems. The analysis reveals that the same control action can be obtained using a much smaller set of control moves via a technique which we term reduced parameterisation.

A compartment model is proposed to describe the HIV infection in humans. The compartments describe the blood, several lymph nodes and connecting lymph vessels. The dynamics in each compartment are described by a simplified HIV model considering the healthy and infected T-cells. A bifurcation analysis based on the variation of the proliferation rate is discussed and supported by simulations. Additional simulations illustrate the effect of a simple mutation model.

Various clinical experiments have suggested the significant role of CD4+ T cells activation in viral spread and immune control of HIV infection. In this paper, we use a new mathematical model to explore the intricate interactions among immune activation, CTL response, T cell depletion, and immune escape. It is shown that enhanced immune activation and proliferation of CD4+ T cells, opposite to its beneficial effects in other infections, may facilitate infection and lead to the depletion of CD4+ T cells if effective immune control is not established. By contrast, once effective CTL response to HIV is mounted, the boost of CD4+ T cell response may be beneficial for controlling infection and alleviating immune impairment. Another finding is that immune escape may occur when the infection rate is low, and enhanced activation may prevent the escape if effective immune control can be established. Simulations are provided to illustrate the theoretical analysis.

This paper studies the problem of channel estimation for the downlink in broadband LTE communications. A Kalman Filter is used to combine channel soundings made with pilot tones that are deployed at different times and in different frequency bands on a pre-selected pattern. This Kalman filter is presented in a form directly suitable for implementation as a periodically time varying filter, in the case where periodic pilot tone data is available. Simulation results illustrate the efficacy of this approach.

In this paper a class of input-parametrized bilinear positive systems is considered. This class is characterized by the fact that the input variables affect only the diagonal entries of the dynamical matrix. The class of systems considered is relevant to a variety of dynamical models arising in system biology and compartmental systems. Given a final time tf, it is proven that the any component of the state vector at tf is a convex functional of the input variables. If a linear cost of the final state is considered this result has the important consequence that any Pontryagin solution of the associated optimal control problem is optimal and can be numerically computed by using standard gradient-type algorithms. A few extensions are given and an example is provided to illustrate the theory.

Preventive diagnosis and maintenance of transformers has become more and more useful in recent times in order to improve the reliability of electric power systems. Time domain dielectric testing techniques such as Return Voltage (RV) measurement and Polarisation-Depolarisation Current (PDC) measurement have recently been widely used as potential tools for condition assessment of transformer insulation. In the frequency domain, measurement of the dissipation factor (tand) over a frequency range of 0.1 mHz to 1 kHz has been commonly used to assess the condition of transformer insulation. A number of transformers have been tested with these diagnostic techniques. A better understanding and analysis of the dielectric test results is only possible with a clear understanding of the physical behaviour of the insulation system in response to moisture and ageing. A circuit model, which describes the dielectric behaviour of the transformer's main insulation system, has been modelled in this paper from the frequency domain measurement data and then RV and PDC data have been simulated from the circuit model. This paper then presents discussions of frequency and time domain techniques to find the condition of transformer insulation in terms of moisture and ageing estimation. ©2009 IEEE.

Several dynamic models of the behaviour of HIV infection are reviewed. Important features of the models examined are the inclusion of the effects of anti-retroviral drugs, virus mutation and latent infection. For the models including virus mutation mathematical analysis yields a complete description of all possible equilibria and their local stability properties. For the cases considered, we can prove that generically, there are only two valid equilibria: (i) the locally unstable uninfected equilibrium and, (ii) the locally stable infected state equilibrium.

This paper deals with temporal enzyme distribution in the activation of biochemical pathways. Pathway activation arises when production of a certain biomolecule is required due to changing environmental conditions. Under the premise that biological systems have been optimized through evolutionary processes, a biologically meaningful optimal control problem is posed. In this setup, the enzyme concentrations are assumed to be time dependent and constrained by a limited overall enzyme production capacity, while the optimization criterion accounts for both time and resource usage. Using geometric arguments we establish the bang-bang nature of the solution and reveal that each reaction must be sequentially activated in the same order as they appear in the pathway. The results hold for a broad range of enzyme dynamics which includes, but is not limited to, Mass Action, Michaelis-Menten and Hill Equation kinetics. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

This work discusses rejection of disturbances with known directions in multivariable control systems. It is shown how frequency domain tradeoffs in multivariable control motivate a design based on disturbance directions. A multivariable design method is presented to design centralized controllers that reject disturbances only in relevant directions. A model of an industrial motion system is used to demonstrate the theory. It is shown how the proposed design method resembles the solution of a competing Hinf design and offers the ability to interpret Hinf centralized control solutions, and understand the tradeoffs inherent in such a design. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

The extended Kalman filter (EKF) has been used in a range of applications for filtering, smoothing, data fusion and related operations. In robot soccer, both self localisation and world modelling benefit substantially from these features. In this paper, we review the application of the EKF to robot soccer. We pay particular attention to the enhancements, tuning and fixes we needed make to the basic algorithm to ensure adequate performance in the competition.

In this paper, we compare and analyse three switched integrator control schemes for integrating plants. The schemes attempt to circumvent a fundamental limitation of linear time invariant (LTI) control, namely, that the closed loop response to a step change in the reference must overshoot if both the controller and the plant contain an integrator. We show that, for a simple example, the switched schemes all have significantly less overshoot than their LTI counterpart. The stability properties of the schemes are also studied. It is first shown that bounded input bounded state stability is guaranteed. Sufficient frequency domain conditions for asymptotic stability are then derived using passivity analysis.

In this paper we consider an alternative approach to implementing Model Predictive Control (MPC). We show that solving a class of quadratic programming (QP) problems is equivalent to solving a class of well-posed nonlinear algebraic loops. These algebraic loops are closely related to that found in static anti-windup synthesis. It therefore follows that certain classes of MPC can be implemented in a form that is a direct generalisation of the standard anti-windup structure. Implementations for classes of MPC are then derived for both regulator and tracking problems. Several alternative iterative algorithms for solving the algebraic loop are then presented. Some simulation results are also provided, with an example computational comparison to active set and interior point based MPC.

This paper studies the optimal tracking performance for linear time-invariant SIMO systems responding to a step reference signal. An integral square error criterion is used as the measure of the tracking performance. First, a formula of the tracking error is derived for stable multivariable systems, which is applicable to both right-invertible and non-right-invertible cases. Then, explicit expressions of the tracking error for SIMO systems are developed. The results show that together with the nonminimum phase zeros and unstable poles of the plant, the variation of the plant direction with frequency also contributes to the tracking difficulty in SIMO systems.

Identification of transformer faults using matched amplitude and phase response characteristics is presented. In frequency response analysis, fault diagnosis is done by detecting changes in frequency response tests. The vast amount of data up to 2 MHz needs to be quantified and characterized for the classification of faults. By a matched fitting with higher order transfer function up to 40, poles, zeros and their relative damping were determined in the frequency plane. Each set of data corresponding to faults is used to train a backpropagation ANN network. Out of 12 faults, the processing technique is able to identify the changes and classify the type of fault for on-line analysis. The location of fault and the severity of faults in the form of more sensitivity are brought out using this signal processing technique.

This paper investigates the scalable input-to-state stability (sISS) property of networks of interconnected systems using the local Lyapunov functions of the individual systems or agents that compose the network. Ensuring sISS of the network prevents the amplification of disturbances through the network, provides uniform transient performance with respect to the number of interconnected systems, and enables network scalability. Our first contribution is to provide sufficient conditions for sISS of networks using sISS vector Lyapunov functions. These sufficient conditions are given in terms of the Lyapunov functions of the agents. We use vector Lyapunov functions, the comparison lemma, and contraction analysis to prove the result. Our second contribution provides conditions for scalable input-to-state stability of weakly coupled interconnected systems. This result allows us to study the scalable input-to-state stability of exponentially stable systems interconnected by weak coupling links. We illustrate the application of the results in four examples.

Dynamic stability across a range of operating conditions and disturbances is an essential requirement in the control of wind turbines. To analyse and design for closed-loop stability, existing methods typically rely on the numerical evaluation of a small-signal model of the system around each operating condition. This approach, however, is an inefficient way to capture and shape dynamic behaviour over the wide ranges of operating conditions and parameter values arising in practical implementations. This work presents an analytic stability analysis for presents an analytic stability analysis for (PMSG) wind turbines. The proposed methodology, based on a Lyapunov function constructed from an analytic expression of the system Jacobian, enables the identification of regions of operation and parameter values for the wind turbine system within which its stability can be guaranteed. A feedback linearisation control strategy is adopted to deal with the nonlinear relationship between the generator speed and the DC-link voltage in the turbine back-to-back converter. The closed-loop response performance of the design based on the proposed methodology is compared to that of a conventional PI control design via simulation tests conducted on a 2 MW turbine model and a 5 MW (PMSG) reference turbine model on the FAST physics-based simulation tool developed by NREL.

This article is concerned with the study of scalability in nonlinear heterogeneous networks affected by communication delays and disturbances. After formalizing the notion of scalability, we give two sufficient conditions to assess this property. Our results can be used to study leader-follower and leaderless networks and allow us to consider the case when the desired configuration of the system changes over time. We show how our conditions can be turned into design guidelines to guarantee scalability and illustrate their effectiveness via numerical examples.

Recent large-scale migration flows from rural areas of the Mekong Delta (MKD) to larger cities in the South-East (SE) region of Vietnam have created the largest migration corridor in the country. This migration trend has further contributed to greater rural¿urban disparities and widened the development gap between regions. In this study, our aim is to understand the migration dynamics and determine the most critical factors affecting the behavior of migrants in the MKD region. We present an agent-based model and incorporate the Theory of Planned Behavior to effectively break down migration intention into related components and contributing factors. A genetic algorithm is used for automated calibration and sensitivity analysis of model parameters, in order to validate our agent-based model. We further explore the migration behavior of people in certain demographic groups and delineate migration flows across cities and provinces from the MKD to the SE region.

The 5-G ultra reliable low latency communication standard is intended, for example, to enable new use cases based on networked feedback control. This article argues why additional delay control and alignment are needed, to meet the well-established feedback control requirements on low end-to-end loop delay and jitter. The main contribution of this article is a novel re-engineered delay aligning data flow controller, where a new static decoupling matrix is introduced. The intention is to obtain a multiple single loop control architecture that allows global robust mathcal {L}2-stability to be proven. The algorithm is suitable to regulate n+1 end-to-end roundtrip delays of a 5-G multiconnectivity connection toward zero pair-wise delay differences. The new stability result is decisive for massive deployment, since weaker results would increase the need for supervision and raise operating costs significantly. A robot arm control loop application operating over three data paths illustrates the performance advantages associated with delay alignment and the proposed algorithm.

© 2015 IEEE. Collective control of a multi-Agent system is concerned with designing strategies for a group of autonomous agents operating in a networked environment. The aim is to achieve a global control objective through distributed sensing, communication, computing, and control. It has attracted many researchers from a wide range of disciplines, including the literature of automatic control. The present paper aims to give a general framework that is able to accommodate many of these outcomes. Within this framework, the development on this topic is systematically reviewed and the representative outcomes can be sorted out from four aspects: (i) agent dynamics, (ii) network topologies, (iii) feedback and communication mechanisms, and (iv) collective behaviors. Thus, the state-of-The-Art approach and technology is described. Moreover, within this framework, further interesting and promising directions on this research topic are envisioned.

Sufficient conditions guaranteeing Lyapunov stability, asymptotic stability and exponential stability of nonlinear two-dimensional continuous-discrete systems are proposed. Special attention is paid to neutrally stable systems such as some two-dimensional system descriptions of vehicle platoons, which may be stable or asymptotically stable but never exponentially stable. Our conditions for Lyapunov stability and asymptotic stability only require the corresponding two-dimensional Lyapunov function to have a negative semidefinite divergence. They are thus suitable for the analysis of non-exponential versions of 2D stability. Examples are given to illustrate the results.

© 1963-2012 IEEE.The paper aims to establish a general framework for robust output synchronization of a group of networked agents. The agents under investigation have nonlinear, uncertain and heterogeneous dynamics. Output synchronization denotes that all agents, through collaborative control, achieve output agreement and follow a desired pattern. In particular, the agreed trajectory is not defined by nor known to any agent in advance. Collaborative control is achieved using only output information from neighboring agents. Two concurrent actions are revealed in the proposed synchronization framework. This framework involves design strategies for both perturbed consensus and perturbed regulation problems, subject to a class of small gain conditions. The success of the framework is verified by constructive proof and numerical simulation.

In this paper, a consensus problem is studied for a group of second-order nonlinear heterogeneous agents with non-uniform time delay in communication links and uncertainty in agent dynamics. We design a class of novel decentralized control protocols for the consensus problem whose solvability is converted into stability analysis of an associated closed-loop system with uncertainty and time delay. Using an explicitly constructed Lyapunov functional, the stability conditions or the solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities apart from a small number of scalar parameters that appear nonlinearly. Furthermore, the linear matrix inequalities are theoretically verified to be solvable when the communication delay is sufficiently small. The effectiveness of the proposed control protocol is illustrated by numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

Output synchronization of heterogeneous multi-agent systems has been one of the most interesting cooperative control problems. This paper first gives a brief survey of the research on the problem from which we see that the problem can be solved in a two-step manner with the aid of a properly designed local reference for each agent: (i) a controller is designed for each agent to achieve the trajectory regulation of the agent output to its associated reference; (ii) network collaboration is added to achieve consensus among references. In the presence of system uncertainties, the robust trajectory regulation problem in (i) can be solved by an internal model design. In this paper, we formulate a novel robust asymptotic model matching problem which is less conservative than trajectory regulation and can be solved by a static controller not relying on an internal model. Moreover, network collaboration is designed in (ii) within the so-called output communication setting such that consensus among references occurs concurrently with robust asymptotic model matching. As a result, output synchronization of heterogeneous multi-agent systems is achieved with a novel approach.

Poor scalability arises in many vehicle platoon problems. Bidirectional strings appear to show some promise for mitigating these problems. In some cases these solutions have the undesirable side effect of non-scalable response to measurement errors. We examine this problem and show how information exchange between neighbouring vehicles may eliminate scalability difficulties due to measurement errors.

In this paper, we consider the problem of disturbance response and error amplification for a simple system of coupled harmonic oscillators. We first suppose that identical oscillators are connected in a string in which each oscillator attempts to track its predecessor by using the same control law that depends on the relative position information from its immediate predecessor. Such an oscillator string is called a homogeneous oscillator string with predecessor-following architecture. Motivated by terminology from the problem of vehicle platooning, we say that the synchronized oscillator system is string unstable if the effect of a disturbance to the lead oscillator is amplified as it propagates along the string. With the use of a new Bode-like integral relation that must be satisfied by the complementary sensitivity function, we provide sufficient conditions for string instability. The sufficient conditions show that any string of oscillators that satisfies certain time domain performance specifications and bandwidth limitations must necessarily be string unstable. We further introduce a concept of time headway for the oscillator system and extend our analysis of string instability to consider the heterogeneous oscillator string and a more general communication range.

A new tool with the potential to verify and track jaw position during delivery has been developed. The method should be suitable for independent quality assurance for jaw position during jaw tracking dynamic IMRT and VMAT treatments. The jaw detection and tracking algorithm developed consists of five main steps. Firstly, the image is enhanced by removing a normalised predicted EPID image (that does not include the collimator transmission) from each cine EPID image. Then, using a histogram clustering technique a global intensity threshold level was determined. This threshold level was used to classify each pixel of the image as either under the jaws or under the MLC. Additionally, the collimator angle was automatically detected and used to rotate the image to vertical direction. Finally, this rotation allows the jaw positions to be determined using vertical and horizontal projection profiles. Nine IMRT fields (with static jaws) and a single VMAT clinical field (with dynamic jaws) were tested by determining the root mean square difference between planned and detected jaw positions. The test results give a detection accuracy of ±1mm RMS error for static jaw IMRT treatments and ±1.5mm RMS error for the dynamic jaw VMAT treatment. This method is designed for quality assurance and verification in modern radiation therapy; to detect the position of static jaws or verify the position of tracking jaws in more complex treatments. This method uses only information extracted from EPID images and it is therefore independent from the linear accelerator.

In this paper, we show how heterogeneous bidirectional vehicle strings can be modelled as port-Hamiltonian systems. Analysis of stability and string stability within this framework is straightforward and leads to a better understanding of the underlying problem. Nonlinear local control and additional integral action is introduced to design a suitable control law guaranteeing l2 string stability of the system with respect to bounded disturbances.

For vehicle platoons, the leader following control architecture is known to be capable of achieving string stability while maintaining tight formations. In this paper, we study a variety of schemes where the leader state is available to the other members of the platoon. We show that in some cases it is possible to achieve string stability in the presence of certain amounts of time delay in the leader state reception. We also compare other properties of the different schemes and discuss some of their advantages and disadvantages. © 2013 The Authors. Published by Elsevier Ltd. All rights reserved.

This paper proposes necessary and sufficient conditions for stability and performance analysis of 2-D mixed continuous-discrete-time systems that can be checked with convex optimization, in particular linear matrix inequalities (LMIs). Specifically, the first contribution of the paper is a condition for exponential stability based on the introduction of a complex Lyapunov function depending polynomially on a parameter and on the use of the Gram matrix method. It is shown that this condition is sufficient for any chosen degree of the complex Lyapunov function, and necessary for an a priori known degree. The second contribution is a non-Lyapunov condition for exponential stability based on eigenvalue products. This condition is necessary and sufficient, and has the advantage of requiring a significantly smaller computational burden for achieving necessity. Lastly, the third contribution is to show how upper bounds on the H8 norm of 2-D mixed continuous-discrete-time systems can be obtained through a semidefinite program based on complex Lyapunov functions. A necessary and sufficient condition is provided for establishing the tightness of the found upper bounds. © 1963-2012 IEEE.

This paper exploits the analogy between the electrical grid and modern communication networks to implement Electric Vehicle (EV) battery charging scheduling algorithms inspired by popular communication network techniques. In preliminary works, a similar approach was used to manage the Grid-to-Vehicle (G2V) active power flows. In this paper, we extend this framework to both implement the Vehicle-to-Grid (V2G) concept and to provide reactive power compensation capabilities that do not affect charging times. The ability of the proposed algorithms to optimally share the available/desired power in a fair way, with minimum communication requirements, in a very uncertain, dynamically changing framework, is illustrated through several examples for different scenarios of interest. © 2014 © 2014 Taylor & Francis.

Positive feedback loops are common regulatory elements in metabolic and protein signalling pathways. The length of such feedback loops determines stability and sensitivity to network perturbations. Here we provide a mathematical analysis of arbitrary length positive feedback loops with protein production and degradation. These loops serve as an abstraction of typical regulation patterns in protein signalling pathways. We first perform a steady state analysis and, independently of the chain length, identify exactly two steady states that represent either biological activity or inactivity. We thereby provide two formulas for the steady state protein concentrations as a function of feedback length, strength of feedback, as well as protein production and degradation rates. Using a control theory approach, analysing the frequency response of the linearisation of the system and exploiting the Small Gain Theorem, we provide conditions for local stability for both steady states. Our results demonstrate that, under some parameter relationships, once a biological meaningful on steady state arises, it is stable, while the off steady state, where all proteins are inactive, becomes unstable. We apply our results to a three-tier feedback of caspase activation in apoptosis and demonstrate how an intermediary protein in such a loop may be used as a signal amplifier within the cascade. Our results provide a rigorous mathematical analysis of positive feedback chains of arbitrary length, thereby relating pathway structure and stability. © 2013 Springer-Verlag Berlin Heidelberg.

HIV mutates rapidly and may develop resistance to specific drug therapies. There is no general agreement on how to optimally schedule the available treatments for mitigating the effects of mutations. With a switched positive linear system, we examined different control strategies applied to a higher order nonlinear mutation model. Simulation results suggest that model predictive control could outperform the common clinical treatment recommendations. This brief is a step forward to develop further tools for helping the practitioners to find the optimal treatment schedule. © 2013 IEEE.

Calcium ions act as messengers in a broad range of processes such as learning, apoptosis, and muscular movement. The transient profile and the temporal accumulation of calcium signals have been suggested as the two main characteristics in which calcium cues encode messages to be forwarded to downstream pathways. We address the analytical quantification of calcium temporal-accumulation in a long, thin section of a nonexcitable cell by solving a boundary value problem. In these expressions we note that the cytosolic Ca2+ accumulation is independent of every intracellular calcium flux and depends on the Ca2+ exchange across the membrane, cytosolic calcium diffusion, geometry of the cell, extracellular calcium perturbation, and initial concentrations. In particular, we analyse the time-integrated response of cytosolic calcium due to i) a localised initial concentration of cytosolic calcium and ii) transient extracellular perturbation of calcium. In these scenarios, we conclude that i) the range of calcium progression is confined to the vicinity of the initial concentration, thereby creating calcium microdomains; and ii) we observe a low-pass filtering effect in the response driven by extracellular Ca2+ perturbations. Additionally, we note that our methodology can be used to analyse a broader range of stimuli and scenarios. © 2004-2012 IEEE.

Induction Heating Furnaces are used extensively in industry. The basic principle is that induced eddy currents are used to heat a ferromagnetic material as it passes through a series of coils. Because of the importance of such systems, there has been on-going interest in their design and operation. Past work includes model development from physical principles and optimal design of operational practices. However, previous work has invariably been based on open-loop strategies. Our work is aimed at the design of a closed-loop control strategy incorporating feedback from the available measurements. This paper reports initial work including model development and calibration together with preliminary control system design. Proposed future work includes full scale industrial implementation.© 2013 Elsevier Ltd. All rights reserved.

The precise mechanism that causes HIV infection to progress to AIDS is still unknown. This paper presents a mathematical model which is able to predict the entire trajectory of the HIV/AIDS dynamics, then a possible explanation for this progression is examined. A dynamical analysis of this model reveals a set of parameters which may produce two real equilibria in the model. One equilibrium is stable and represents those individuals who have been living with HIV for at least 7 to 9 years, and do not develop AIDS. The other one is unstable and represents those patients who developed AIDS in an average period of 10 years. However, further work is needed since the proposed model is sensitive to parameter variations. © 2011 IFAC.

This paper is motivated by the study of mutation in HIV infection. Combination antiretroviral therapy slows the clinical progression of HIV infection, however drug resistance due to viral mutation is a challenging problem. Some studies have speculated that alternating between drug regimens on a fixed schedule might forestall therapeutic failure. To further analyze this speculation, we consider a model of 64 viral strains with 3 drug combinations to analyze drug regimens to maximise the delay till viral escape. A model predictive control scheme is proposed for determining near optimal switching drug schedules. This technique is compared with an optimal control approach and with the strategy commonly used in clinical practice. © 2011 IFAC.

Designing suitable robotic controllers for automating movement-based rehabilitation therapy requires an understanding of the interaction between patient and therapist. Current approaches do not take into account the highly dynamic and interdependent nature of this relationship. A better understanding can be accomplished through framing the interaction as a problem in game theory. The main strength behind this approach is the potential to develop robotic control systems which automatically adapt to patient interaction behavior. Agents learn from experiences, and adapt their behaviors so they are better suited to their environment. As the models evolve, structures, patterns and behaviors emerge that were not explicitly programmed into the original models, but which instead surface through the agent interactions with each other and their environment. This paper advocates the use of such agent based models for analysing patient-therapist interactions with a view to designing more efficient and effective robotic controllers for automated therapeutic intervention in motor rehabilitation. The authors demonstrate in a simplified implementation the effectiveness of this approach through simulating known behavioral patterns observed in real patient-therapist interactions, such as learned dependency. © 2011, IGI Global.

The optimal control problem for a particular class of switched systems is addressed in this paper. Using a linear co-positive cost function, a necessary and sufficient condition for optimal control is derived. Optimal states and costates can lie on a sliding surface, and this corresponds to a chattering switching law. Due to the complexity of exact solution of the general optimal control problem, we introduce a suboptimal, guaranteed cost algorithm, associated with the optimal problem. These results are then applied to a simplified model of HIV viral mutation dynamics, which under simplifying assumptions can be viewed as a positive switched linear system. Simulations compare the optimal switching control law with the sub-optimal guaranteed cost approach. © 2010 IFAC.

A mathematical model is developed to further flexamine the dynamic interaction of uninfected T cells with Human Immunodeficiency Virus (HIV) mutations. We study how the dynamics are affected by immune response to infected cells under intermittent antiretroviral therapy. Our goal is to analyze the SMART (Strategies for Management of Anti-Retroviral Therapy) study outcomes and based on that try to identify possible causes of its failure. We mathematically describe the HIV infection and perform numerical simulation to approach the course of the disease. Preliminary results suggest that the scheduling of follow-up visits and working range of CD4+ T cells count used during the SMART study could flexplain the observed adverse outcomes in that trial. © 2009 IFAC.

Last December 13-15 2006 at the Manchester Grand Hyatt Hotel in San Diego, California, the IEEE Conference on Decision and Control (CDC) marks its 45th conference. The conference had its usual technical program, preconference and education workshop, interactive presentations, semiplenary talks and bode lecture, a ceremony and conference banquet, and finally an acknowledgement to end the program.

Preventative diagnosis and maintenance of transformers has become more popular in recent times in order to improve the reliability of electric power systems. A number of transformers have recently been tested using Return Voltage (RV) and Dielectric Dissipation Factor (tand) measurements in the time and frequency domain, respectively. This paper outlines a circuit model which describes the dielectric behaviour of the transformer insulation system and has been parameterised from the frequency domain data. This model was then used to simulate RV and Polarisation-Depolarisation current (PDC) results. Some recommendations about the diagnosis of the transformers have been proposed. © Institution of Engineers.

The expanding integration of control and communication networks in recent years has generated an increasing interest in control problems with feedback over a communication channel. Significant research activity has concentrated on stabilisation in face of channel effects such as quantisation and data-rate limits. in a recent paper, the authors have studied the problem of feedback stabilisation over a communication channel with a constraint on the admissible signal-to-noise ratio (SNR). It has been shown therein that for a delay-free, linear time-invariant feedback loop, a SNR constraint in the feedback channel imposes fundamental limitations in the ability to achieve closed-loop stability. The present paper extends these results by introducing a time-delay in the loop, and shows that the lowest SNR required for closed-loop stability increases by a factor that may grow exponentially with the time-delay and the unstable open loop poles of the system. This result contributes to the quantification of performance trade offs in integrated control and communication environments. Copyright © 2005 IFAC.

A systematic evaluation procedure for the choice of sampling rate and anti-alias filter in sampled-data control is presented. It is based on a multi criteria H8 optimization procedure, where sampled-data measures are introduced to capture the intersample behavior. The optimization scheme is based on linear matrix inequalities (LMIs) formulated in the delta operator, and the result is a low order controller of PID type. Both low frequency performance, mid frequency stability margins and high frequency control activity are taken into account. The evaluation procedure suggests to use higher sampling rates than typical text books recommend. Copyright © 2005 IFAC.

A procedure for H8 optimization of low order controllers for discrete-time and sampled-data systems is presented in this paper. Generally, low order H8 controllers may be achieved by solving bilinear matrix inequalities (BMIs). In this paper an iterative alternation between two LMIs gives a suboptimal solution. To avoid local minima in this search the initial controller is obtained by a frequency weighted controller reduction scheme, where the closed loop properties of a full order controller is taken into account. A minimal number of parameters in the state space realization of the controller also reduces the complexity and improves numerical robustness. The complete presentation is based on delta operator models, which shows a close relationship between the continuous- and discrete-time solutions. The sensitivity of the ordinary discrete-time shift operator LMI formulation to small sampling periods is also analyzed.

A unified and general framework is presented for H8 control of mixed continuous-time and discrete-time time-varying (periodic) systems. Using the delta operator a close relationship is shown between the continuous- and discrete-time solutions. No assumptions are made on certain system matrices being zero or normalized, which makes the approach general and easy to apply. A combined continuous/discrete-time lifting procedure is shown to be useful, especially for illconditioned systems. This procedure together with the delta formalism results in a numerically robust design method concerning both short and long sampling periods for systems with ill-conditioned dynamics, including widely spread eigenvalues.

Two anti-windup schemes for discrete time systems to achieve global stability and induced l2 performance are presented. The first scheme is a direct extension of an existing static anti-windup scheme for continuous systems. As in continuous time, a problem of implementing an algebraic loop formed arises. However, while preserving the stability and performance, an iterative algorithm to solve the algebraic loop within its prescribed time sampling may be employed. Alternatively, a closely related explicit static anti-windup scheme is proposed, in which no iterative solution at each time step is required. Simulation results are given for both schemes.

We recently considered feedback stabilization over a Signal to Noise Ratio (SNR) constrained channel. The results were examined for the state feedback and minimum phase cases, with links to bit-rate limited control. In this paper, we extend this analysis to Non-Minimum Phase (NMP) plants, and show that for Linear Time Invariant (LTI) control, NMP zeros further constrain the ability to stabilize over an SNR limited channel. This differs from the situation of bit-rate limited stabilization where NMP zeros do not play a role. We show that by considering linear time varying feedback the effect of NMP zeros in SNR limited stabilization may be eliminated.

We consider ill-conditioned two-input two-output (TITO) plants whose singular value decomposition (SVD) is independent of frequencies. For such plants we design a static anti-windup PI controller based on reverse frame (RF) approach. It has also been shown that this design approach results in a closely related controller structure with the static anti-windup controller design based on linear matrix inequality (LMI) optimisation. Furthermore, this simple design approach gives an explicit anti-windup implementation with good robustness properties. The simulation example also shows that this implementation allows independent controller and anti-windup design. The extension of these ideas to higher dimensional systems appears to be problematic at this point.

In this paper we study the problem of tracking a step reference signal using sampled-data control systems. We investigate the best achievable tracking performance, where the performance is deemed best for it is the minimal attainable by all possible sampled-data stabilizing controllers. Our primary objective is to investigate the fundamental tracking performance limit in sampled-data systems, and to understand whether and how sampling and hold in a sampled-data system may impose intrinsic barriers to performance. For this optimal tracking performance. The result shows that a performance loss is generally incurred in a sampled-data system, in comparison to the tracking performance achievable by continuous-time controllers. This loss of performance, as so demonstrated by the expression, can be attributed to the non-minimum behaviors and the aliasing effects generated by samplers and hold devices.

The prevalent method used to determine the Ground Potential Rise (GPR) of an earthing or grounding system is to perform a Fall of Potential (FOP) test undertaken during an grounding system current injection test. Determining the test GPR requires analysis of FOP test data due to the FOP response's non-conservative asymptotic behaviour. This paper assesses achievable tolerance by FOP test analysis including recognised and alternative methods. Susceptibility to voltage and distance measurement noise is examined by application to an grounding system model to establish minimum error bounds and method estimation variation on GPR estimates. The applicability of the FOP test 'rule of thumb' termination condition, to take three to four readings beyond the 'knee' of the FOP response, is also examined. In particular, the question of whether appropriate information is gathered when this condition is met is discussed.

For strict-feedback nonlinear systems, this paper shows that it is impossible to reduce to zero the optimal cost in the regulation of more states than the number of control inputs in the system, even using unrestricted control effort. By constructing a near optimal cheap control law, we characterise the infirm value of the optimal regulation cost as the optimal value of a reduced-order regulator problem where the states with lower relative degree drive those with higher relative degree. We illustrate our results with two examples of practical interest: the optimal regulation of the rotational motion of a free rigid body, and the optimal control of a magnetic suspension system.

This paper develops exact, computable formulas for the frequency gain and L2-induced norm of the sensitivity operator in a sampled-data control system. With sampled data, we refer to a system that combines both continuous-time and discrete-time signals, which is studied in continuous time. The expressions are obtained using lifting techniques in the frequency domain and have application in performance and stability robustness analysis taking into account full intersample information.