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Volume 153
Issue 5
IEE Proceedings - Control Theory and Applications
Volume 153, Issue 5, September 2006
Volumes & issues:
Volume 153, Issue 5
September 2006
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- Author(s): Robert Shorten and Kumpati S. Narendra
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 504 –505
- DOI: 10.1049/ip-cta:20069014
- Type: Article
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p.
504
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- Author(s): A. Leizarowitz ; R. Stanojević ; R. Shorten
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 506 –519
- DOI: 10.1049/ip-cta:20050171
- Type: Article
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p.
506
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The stochastic properties of a class of communication networks whose dynamics are Markovian are analysed. The asymptotic behaviour of such a network in terms of the first and second moments of a stochastic process that describes the network dynamics is characterised and tools for their calculation are provided. Specifically, computation techniques for the calculation of these statistics are provided and that these algorithms converge exponentially fast is shown. Finally, how the results may be used for the design of network routers to realise networks with desired statistical properties is suggested. - Author(s): J.P. Hespanha
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 520 –535
- DOI: 10.1049/ip-cta:20050088
- Type: Article
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p.
520
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The author describes a model for stochastic hybrid systems (SHSs) where transitions between discrete modes are triggered by stochastic events. The rate at which these transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Several examples of SHSs arising from a varied pool of application areas are discussed. These include the modelling of transmission control protocol (TCP) algorithm for congestion control both for long-lived and on–off flows, state-estimation for networked control systems, and the stochastic modelling of chemical reactions. These examples illustrate the use of SHSs as a modelling tool. Attention is mostly focused on polynomial stochastic hybrid systems (pSHSs) that generally correspond to SHSs with polynomial continuous vector fields, reset maps and transition intensities. For pSHSs, the dynamics of the statistical moments of the continuous states evolve according to infinite-dimensional linear ordinary differential equations (ODEs). It is shown that these ODEs can be approximated by finite-dimensional non-linear ODEs with arbitrary precision. Based on this result, a procedure to build this type of approximations for certain classes of pSHSs is provided. This procedure is applied to several examples and the accuracy of the results obtained is evaluated through comparisons with Monte Carlo simulations. - Author(s): J. Bakkeheim and T.A. Johansen
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 536 –545
- DOI: 10.1049/ip-cta:20050161
- Type: Article
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p.
536
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Multiple model adaptive control (MMAC) is a well-established approach for implementing adaptive systems with fast transient response. The authors consider a recently developed MMAC method based on adaptive nonlinear backstepping control where the parameter estimate may be instantaneously reset based on a criterion that requires a negative jump in the associated control Lyapunov function. Particular attention is paid to the transient effects of data filtering, which must be introduced in any practical implementation of the MMAC algorithm in order to reduce the sensitivity to noise, disturbances and model uncertainty. Insight into the robust behaviour of the adaptive system resulting from the filtering and an investigation into the trade-offs between high transient performance and robustness to uncertainty is the main aim of the authors who also suggest data filter tuning guidelines and illustrate the results using a simulation example. - Author(s): K.S. Narendra ; N. Oleng ; S. Mukhopadhyay
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 546 –555
- DOI: 10.1049/ip-cta:20050284
- Type: Article
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546
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The adaptive control of strictly decentralised adaptive control systems has been investigated in the past and it has been demonstrated that, under very general conditions, exact asymptotic tracking by the different subsystems can be achieved without any communication between them. Here, the problem is discussed when communication between the different subsystems is permitted. The problems considered range from totally decentralised control to totally centralised control with emphasis on partial communication. In all cases, the problems can be posed as ones related to the stability of switching systems. The principal theoretical contribution is the demonstration that the overall system is globally stable, resulting in exact asymptotic tracking by all the subsystems. Decoupling stability and performance issues permit the designer to focus on improving the behaviour of the overall system. The principal practical contribution is the demonstration that significant improvement in transient responses of the subsystems can be achieved with communication at relatively few instants of time. - Author(s): I. Hwang ; H. Balakrishnan ; C. Tomlin
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 556 –566
- DOI: 10.1049/ip-cta:20050053
- Type: Article
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p.
556
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The problem of estimating the discrete and continuous state of a stochastic linear hybrid system, given only the continuous system output data, is studied. Well established techniques for hybrid estimation, known as the multiple model adaptive estimation algorithm, and the interacting multiple model algorithm, are first reviewed. Conditions that must be satisfied to guarantee the convergence of these hybrid estimation algorithms are then presented. These conditions also provide a means to predict, as a function of the system parameters, which transitions in a hybrid system are relatively easy to detect. A new variant of hybrid estimation algorithms, called the residual-mean interacting multiple model (RMIMM) algorithm, is then proposed and analysed. The performance of RMIMM is demonstrated through multi-modal aircraft trajectory tracking examples. - Author(s): A. Rantzer
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 567 –574
- DOI: 10.1049/ip-cta:20050094
- Type: Article
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567
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In order to simplify computational methods based on dynamic programming, a relaxed procedure based on upper and lower bounds of the optimal cost was recently introduced. The convergence properties of this procedure are analysed here. In particular, it is shown that the computational effort in finding an approximately optimal control law by relaxed value iteration is related to the polynomial degree that is needed to approximate the optimal cost. This gives a rigorous foundation for the claim that the search for optimal control laws requires complex computations only if the optimal cost function is complex. A computational example is given for switching control on a graph with 60 nodes, 120 edges and 30 continuous states. - Author(s): M.S. Branicky ; M.M. Curtiss ; J. Levine ; S. Morgan
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 575 –590
- DOI: 10.1049/ip-cta:20050152
- Type: Article
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p.
575
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A sampling-based approach to planning, control and verification inspired by robotics motion planning algorithms such as rapidly exploring random trees (RRTs) and probabilistic roadmaps (PRMs) is surveyed. With the focus on RRTs, how to adapt them to solve standard non-linear control problems is demonstrated. RRTs are extended to purely discrete spaces (replacing distance metrics with cost-to-go heuristic estimates and substituting local planners for straight-line connectivity) and computational experiments comparing them to conventional methods, such as A* are provided. Finally, RRTs are extended to the case of hybrid systems and our modifications to LaValle's motion strategy library to allow for hybrid planning and verification are described. The work on the coverage and optimality properties of sampling-based techniques is also reviewed. - Author(s): T. Moor ; J.M. Davoren ; J. Raisch
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 591 –599
- DOI: 10.1049/ip-cta:20050347
- Type: Article
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p.
591
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The synthesis of discrete event controllers for given continuous dynamics is studied within the hybrid system theory and its applications. A common approach involves the generation of a discrete abstraction of the continuous plant model, thus transforming the hybrid control problem into a purely discrete one that is then addressable using methods from the discrete event systems theory. In previous work, conditions were derived guaranteeing that successful synthesis on the abstraction level would provide a solution for the underlying hybrid problem. If synthesis failed, however, the abstraction was in need of refinement. This resulted in an iterative procedure alternating abstraction refinement with trial controller synthesis. The authors now use a temporal decomposition of the control problem to extract relevant diagnostic information when the synthesis step fails. In contrast with standard unfocused and global refinement strategies, the new iteration ‘learns by doing’ in the synthesis step and implements a refinement that is tailored to the particular hybrid plant and specification at hand.
Editorial: Special Section on Hybrid systems
Tools for the analysis and design of communication networks with Markovian dynamics
Modelling and analysis of stochastic hybrid systems
Transient performance, estimator resetting and filtering in nonlinear multiple model adaptive backstepping control
Decentralised adaptive control with partial communication
State estimation for hybrid systems: applications to aircraft tracking
Relaxed dynamic programming in switching systems
Sampling-based planning, control and verification of hybrid systems
Learning by doing: systematic abstraction refinement for hybrid control synthesis
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- Author(s): S.J. Kwon
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 600 –606
- DOI: 10.1049/ip-cta:20050452
- Type: Article
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p.
600
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A robust Kalman filtering method is suggested by adopting a perturbation estimation process which is to reconstruct total uncertainty with respect to the nominal state equation of a physical system. The predictor and corrector of the discrete Kalman filter are reformulated with the perturbation estimator. In succession, the state and perturbation estimation error dynamics and the covariance propagation equations are derived. In the sequel, the recursive algorithm of combined discrete Kalman filter and perturbation estimator is obtained. The proposed robust Kalman filter has the property of integrating innovations and the adaptation capability to the time-varying uncertainties. An example of application to a mobile robot is shown to validate the performance of the proposed scheme. - Author(s): L. Ou ; W. Zhang ; D. Gu
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 607 –614
- DOI: 10.1049/ip-cta:20050463
- Type: Article
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p.
607
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The procedures for determining the complete sets of stabilising proportional integral derivative (PID) controllers are presented for three classes of second-order integrating processes with time delay. The necessary condition for the PID controllers to stabilise second-order integrating processes with time delay is first derived in the case where frequency, ω, equals zero or infinity. On the basis of the extended Hermite–Biehler theorem, analytical formulas are provided to determine the admissible ranges of the proportional gain (kp), integral gain (ki) and the derivative gain (kd), respectively, and the complete set of stabilising PID controllers is found by sweeping over the entire range of allowable kp values. The stability analysis on the basis of the extended Hermite–Biehler theorem shows that the stability boundary in the controller parameter space depends only on the frequencies in the defined small range. In view of this, the sets of stabilising PID controllers are also determined by sweeping over the admissible ranges of kd and ki, respectively. As a result, for a given second-order integrating process with time delay, the complete set of stabilising PID controllers can be determined by sweeping any one of the PID parameters over the corresponding admissible range. - Author(s): M.-T. Ho and Y.-W. Tu
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 615 –622
- DOI: 10.1049/ip-cta:20050070
- Type: Article
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p.
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The application of the H∞ proportional-integral-derivative (PID) control synthesis method to tip position control of a flexible-link manipulator is investigated. For this system, it is first shown that the classical PID tuning formula may yield poor closed-loop performance. This underlines the need for a rigorous PID control synthesis methodology for this infinite-dimensional and non-minimum-phase system. To achieve high performance in PID control, this particular control design problem is cast into the H∞ framework. On the basis of a recently proposed H∞ PID control synthesis method, a set of admissible controllers is then obtained to be robust against uncertainty introduced by neglecting the higher-order modes of the link and to achieve the desired time-response specifications. The most important feature of the H∞ PID control synthesis method is its ability to provide the knowledge of the entire admissible PID controller gain space, which can facilitate controller fine tuning. Finally, experimental results are given to demonstrate the effectiveness of the H∞ PID control. - Author(s): Z. Zuo and Y. Wang
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, p. 623 –626
- DOI: 10.1049/ip-cta:20045258
- Type: Article
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p.
623
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The problem of robust stability for linear time-delay systems under nonlinear perturbations is discussed. The delay is assumed to be time-varying. A less conservative delay-dependent robust stability condition is derived by using some free matrices to express the relationship of the terms in the Leibniz–Newton formula within the framework of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method. - Author(s): Q. Fu ; G. Xie ; L. Wang
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, page: 627 –627
- DOI: 10.1049/ip-cta:20045170
- Type: Article
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- Author(s): G. Guo
- Source: IEE Proceedings - Control Theory and Applications, Volume 153, Issue 5, page: 628 –628
- DOI: 10.1049/ip-cta:20050328
- Type: Article
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p.
628
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Robust Kalman filtering with perturbation estimation process for uncertain systems
Sets of stabilising PID controllers for second-order integrating processes with time delay
Position control of a single-link flexible manipulator using H∞-based PID control
New stability criterion for a class of linear systems with time-varying delay and nonlinear perturbations
Comment: Controllability of periodic systems: continuous and discrete
Reply: Controllability of periodic systems: continuous and discrete
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