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Automatic Control, IEEE Transactions on

Issue 10 • Date Oct. 2010

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Displaying Results 1 - 25 of 33
  • Table of contents

    Page(s): C1 - C4
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  • IEEE Control Systems Society

    Page(s): C2
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  • Scanning the issue

    Page(s): 2217 - 2218
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  • A Scalable Robust Stability Criterion for Systems With Heterogeneous LTI Components

    Page(s): 2219 - 2234
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (973 KB) |  | HTML iconHTML  

    A scalable robust stability criterion for interconnected systems with heterogeneous linear time-invariant components is presented in this paper. The criterion involves only the properties of individual components and the spectrum of the interconnection matrix, which can be verified with relatively low computational effort, and more importantly maintains scalability of the analysis. Our main result shows that if the components are single-input-single-output (SISO), then the criterion has an appealing graphical interpretation which resembles the classical Nyquist criterion. View full abstract»

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  • Stochastic Averaging in Continuous Time and Its Applications to Extremum Seeking

    Page(s): 2235 - 2250
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (627 KB) |  | HTML iconHTML  

    We investigate stochastic averaging theory in continuous time for locally Lipschitz systems and the applications of this theory to stability analysis of stochastic extremum seeking algorithms. First, we establish a general stochastic averaging principle and some related stability theorems for a class of continuous-time nonlinear systems with stochastic perturbations and remove or weaken several significant restrictions present in existing results: global Lipschitzness of the nonlinear vector field, equilibrium preservation under the stochastic perturbation, global exponential stability of the average system, and compactness of the state space of the perturbation process. Then, we propose a continuous-time extremum seeking algorithm with stochastic excitation signals instead of deterministic periodic signals. We analyze the stability of stochastic extremum seeking for static maps and for general nonlinear dynamic systems. View full abstract»

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  • A Linear Representation of Dynamics of Boolean Networks

    Page(s): 2251 - 2258
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    A new matrix product, called semi-tensor product of matrices, is reviewed. Using it, a matrix expression of logic is proposed, where a logical variable is expressed as a vector, a logical function is expressed as a multiple linear mapping. Under this framework, a Boolean network equation is converted into an equivalent algebraic form as a conventional discrete-time linear system. Analyzing the transition matrix of the linear system, formulas are obtained to show a) the number of fixed points; b) the numbers of cycles of different lengths; c) transient period, for all points to enter the set of attractors; and d) basin of each attractor. The corresponding algorithms are developed and used to some examples. View full abstract»

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  • Analysis of Lyapunov Method for Control of Quantum States

    Page(s): 2259 - 2270
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (789 KB) |  | HTML iconHTML  

    The natural trajectory tracking problem is studied for generic quantum states represented by density operators. A control design based on the Hilbert-Schmidt distance as a Lyapunov function is considered. The control dynamics is redefined on an extended space where the LaSalle invariance principle can be correctly applied even for non-stationary target states. LaSalle's invariance principle is used to derive a general characterization of the invariant set, which is shown to always contain the critical points of the Lyapunov function. Critical point analysis of the latter is used to show that, for generic states, it is a Morse function with n! isolated critical points, including one global minimum, one global maximum and n!-2 saddles. It is also shown, however, that the actual dynamics of the system is not a gradient flow, and therefore a full eigenvalue analysis of the linearized dynamics about the critical points of the dynamical system is necessary to ascertain stability of the critical points. This analysis shows that a generic target state is locally asymptotically stable if the linearized system is controllable and the invariant set is regular, and in fact convergence to the target state (trajectory) in this case is almost global in that the stable manifolds of all other critical points form a subset of measure zero of the state space. On the other hand, if either of these sufficient conditions is not satisfied, the target state ceases to be asymptotically stable, a center manifold emerges around the target state, and the control design ceases to be effective. View full abstract»

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  • Stable LPV Realization of Parametric Transfer Functions and Its Application to Gain-Scheduling Control Design

    Page(s): 2271 - 2281
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (832 KB) |  | HTML iconHTML  

    The paper deals with the stabilizability of linear plants whose parameters vary with time in a compact set. First, necessary and sufficient conditions for the existence of a linear gain-scheduled stabilizing compensator are given. Next, it is shown that, if these conditions are satisfied, any compensator transfer function depending on the plant parameters and internally stabilizing the closed-loop control system when the plant parameters are constant, can be realized in such a way that the closed-loop asymptotic stability is guaranteed under arbitrary parameter variations. To this purpose, it is preliminarily proved that any transfer function that is stable for all constant parameters values admits a realization that is stable under arbitrary parameter variations (linear parameter-varying (LPV) stability). Then, the Youla-Kucera parametrization of all stabilizing compensators is exploited; precisely, closed-loop LPV stability can be ensured by taking an LPV stable realization of the Youla-Kucera parameter. To find one such realization, a reasonably simple and general algorithm based on Lyapunov equations and Cholesky's factorization is provided. These results can be exploited to apply linear time-invarient design to LPV systems, thus achieving both pointwise optimality (or pole placement) and LPV stability. Some potential applications in adaptive control and online tuning are pointed out. View full abstract»

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  • Realization Theory for Linear Hybrid Systems

    Page(s): 2282 - 2297
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (605 KB) |  | HTML iconHTML  

    The paper develops realization theory for linear hybrid systems, i.e., hybrid systems in continuous-time without guards whose continuous dynamics is determined by linear control systems and whose discrete dynamics is determined by a finite-state automaton. We will formulate necessary and sufficient conditions for the existence of a realization. We will show that minimality is equivalent to observability and span-reachability, and that minimal systems are isomorphic. In turn, observability and span-reachability can be characterized by rank conditions. View full abstract»

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  • The Cost of Complexity in System Identification: Frequency Function Estimation of Finite Impulse Response Systems

    Page(s): 2298 - 2309
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    In this paper, we consider full order modeling, i.e., when the true system belongs to the model set. We investigate the minimum amount of input energy required to estimate a given linear system with a full order model within a prescribed degree of accuracy γ, as a function of the model complexity. This quantity we define to be the “cost of complexity.” The degree of accuracy is measured by the inverse of the maximum variance of the discrete-time frequency function estimator over a given frequency range [-ωBB]. It is commonly believed that the cost increases as the model complexity increases. However, the amount of information that is to be extracted from the system also influences the cost. The objective of this paper is to quantify these dependencies for systems described by finite-impulse response models. It is shown that, asymptotically in the model order n and sample size, the cost is well approximated by γσo2B/π where σo2 is the noise variance. This expression can be used as a simple rule of thumb for assessing trade-offs that have to be made in a system identification project where full order models are used. For example, for given experiment duration, excitation level and desired accuracy, one can assess how the achievable frequency range depends on the required model order. This type of consideration is useful when formally planning experiments. In addition, we establish several properties of the cost of complexity. We find, for example, that if ωB is very close (but not necessarily equal) to π, the optimal input satisfies the model quality constraint for all frequencies. View full abstract»

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  • Types of Asynchronous Diagnosability and the Reveals-Relation in Occurrence Nets

    Page(s): 2310 - 2320
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (639 KB) |  | HTML iconHTML  

    We consider asynchronous diagnosis in (safe) Petri net models of distributed systems, using the partial order semantics of occurrence net unfoldings. Both the observability and diagnosability properties will appear in two different forms, depending on the semantics chosen: strong observability and diagnosability are the classical notions from the state machine model and correspond to interleaving semantics in Petri nets. By contrast, the weak form is linked to characteristics of nonsequential processes, and requires an asynchronous progress assumption on those processes. We give algebraic characterizations for both types, and give verification methods. The study of weak diagnosability leads us to the analysis of a relation in occurrence nets, first presented in : given the occurrence of some event a that reveals b, the occurrence of b is inevitable. Then b may already have occurred, be concurrent to, or even in the future of a. We show that the reveals-relation can be effectively computed recursively-for each pair, a suitable finite prefix of bounded depth is sufficient-, and show its use in asynchronous diagnosis. Based on this relation, a decomposition of the Petri net unfolding into facets is defined, yielding an abstraction technique that preserves and reflects maximal partially ordered runs. View full abstract»

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  • Model Reduction by Moment Matching for Linear and Nonlinear Systems

    Page(s): 2321 - 2336
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (607 KB) |  | HTML iconHTML  

    The model reduction problem for (single-input, single-output) linear and nonlinear systems is addressed using the notion of moment. A re-visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment. This, in turn, is used to pose and solve the model reduction problem by moment matching for nonlinear systems, to develop a notion of frequency response for nonlinear systems, and to solve model reduction problems in the presence of constraints on the reduced model. Connections between the proposed results, projection methods, the covariance extension problem and interpolation theory are presented. Finally, the theory is illustrated by means of simple worked out examples and case studies. View full abstract»

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  • H_{\infty } Positive Filtering for Positive Linear Discrete-Time Systems: An Augmentation Approach

    Page(s): 2337 - 2342
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (280 KB) |  | HTML iconHTML  

    In this note, we address the reduced-order positive filtering problem of positive discrete-time systems under the H performance. Commonly employed approaches, such as linear transformation and elimination technique, may not be applicable in general due to the positivity constraint of the filter. To cope with the difficulty, we first represent the filtering error system as a singular system by means of the system augmentation approach, which will facilitate the consideration of the positivity constraint. Two necessary and sufficient conditions are obtained in terms of matrix inequalities under which the filtering error system has a prescribed H performance. Then, a necessary and sufficient condition is proposed for the existence of the desired positive filters, and an iterative linear matrix inequality (LMI) algorithm is presented to compute the filtering matrices, which can be easily checked by standard software. Finally, a numerical example to illustrate the effectiveness of the proposed design procedures is presented. View full abstract»

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  • A Negative Imaginary Lemma and the Stability of Interconnections of Linear Negative Imaginary Systems

    Page(s): 2342 - 2347
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (214 KB) |  | HTML iconHTML  

    The note is concerned with linear negative imaginary systems. First, a previously established Negative Imaginary Lemma is shown to remain true even if the system transfer function matrix has poles on the imaginary axis. This result is achieved by suitably extending the definition of negative imaginary transfer function matrices. Secondly, a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems. Meanwhile, some properties of linear negative imaginary systems are developed. Finally, an undamped flexible structure example is presented to illustrate the theory. View full abstract»

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  • Dynamical Analysis of Neural Networks of Subgradient System

    Page(s): 2347 - 2352
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (341 KB) |  | HTML iconHTML  

    In this technical note, we consider a class of neural network, which is a generalization of neural network models considered in the optimization context. Under some mild assumptions, this neural network can be translated into a negative subgradient dynamical system. At first, we study the existence and uniqueness of solution of this neural network. Then, by nonsmooth Łojasiewicz inequality, we prove the convergence of the trajectories of this neural network. In the end, a constrained minimization problem is studied, which can be associated with this neural network. It is proved that the local constrained minimum of the cost function coincides with the stable equilibria point of this neural network. View full abstract»

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  • Robust Stability of Time-Varying Uncertain Systems With Rational Dependence on the Uncertainty

    Page(s): 2353 - 2357
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    Robust stability of time-varying uncertain systems is a key problem in automatic control. This note considers the case of linear systems with rational dependence on an uncertain time-varying vector constrained in a polytope, which is typically addressed in the literature by using the linear fractional representation (LFR). A novel sufficient condition for robust stability is derived in terms of a linear matrix inequality (LMI) feasibility test by exploiting homogeneous polynomial Lyapunov functions, the square matrix representation and an extended version of Polya's theorem which considers structured matrix polynomials. It is shown that this condition is also necessary for second-order systems, and that this condition is less conservative than existing LMI conditions based on the LFR for any order. View full abstract»

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  • Adaptive Control for Uncertain Continuous-Time Systems Using Implicit Inversion of Prandtl-Ishlinskii Hysteresis Representation

    Page(s): 2357 - 2363
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    In this note, an implicit inversion approach is introduced to avoid difficulties associated with stability analysis in the direct application of inversion for operator-based hysteresis models. Based on this implicit inversion, an adaptive control algorithm is formulated for continuous-time linear dynamical systems preceded with hysteresis nonlinearities described by the Prandtl-Ishlinskii model. A stability analysis of the controlled system is performed to show that zero-output tracking error can be achieved. Simulation results show the effectiveness of the proposed algorithm. View full abstract»

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  • Linear Moving Horizon Estimation With Pre-Estimating Observer

    Page(s): 2363 - 2368
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (219 KB) |  | HTML iconHTML  

    In this note, a moving horizon estimation (MHE) strategy for detectable linear systems is proposed. Like the idea of “pre-stabilizing” model-predictive control, the states are estimated by a forward simulation with a pre-estimating observer in the MHE formulation. Compared with standard linear MHE approaches, it has more degrees of freedom to optimize the noise filtering. Tuning parameters are chosen to minimize the effects of measurement noise and model errors, which is implemented by finding tightest estimation error bounds. The performance of the proposed observer is demonstrated on one linear discrete-time example. View full abstract»

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  • Reduced-Order Observer in the Sliding-Mode Control of Nonlinear Nonaffine Systems

    Page(s): 2368 - 2373
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    The note considers the variable-structure control of nonlinear known nonaffine systems when the state vector is not completely available and the use of observers is required. The strategy of introducing integrators in the input channel is exploited to enlarge the class of tractable control systems. A new reduced-order observer is proposed and conditions are found under which it is proven the convergence to the unique ideal solution of both system and observer. The control problem is solved by forcing a sliding regime for the observer, while satisfying an exponential stability criterion for the observation error state equation. View full abstract»

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  • Minimum Data Rate for Mean Square Stabilization of Discrete LTI Systems Over Lossy Channels

    Page(s): 2373 - 2378
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (251 KB) |  | HTML iconHTML  

    This note investigates the minimum data rate for mean square stabilization of discrete linear time-invariant systems over a lossy channel. The packet dropout process of the channel is modeled as an independent and identically distributed process. For general single input systems, the minimum data rate is explicitly given in terms of unstable eigenvalues of the open loop matrix and the packet dropout rate, which clearly reveals the amount of the additional bit rate required to counter the effect of packet dropouts on stabilization. Sufficient data rate conditions for the mean square stabilization of multiple input systems are derived as well. View full abstract»

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  • Geometric Analysis of the Formation Problem for Autonomous Robots

    Page(s): 2379 - 2384
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (262 KB) |  | HTML iconHTML  

    In the formation control problem for autonomous robots, a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a Lyapunov-based approach. Besides the target formation, the closed-loop dynamics of the robots feature various other undesired invariant sets such as nonrigid formations. This note addresses a global stability analysis of the closed-loop formation control dynamics. We pursue a differential geometric approach and derive purely algebraic conditions for local stability of invariant embedded submanifolds. These theoretical results are then applied to the well-known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation. View full abstract»

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  • Stability of Time-Delay Feedback Switched Linear Systems

    Page(s): 2385 - 2390
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (276 KB) |  | HTML iconHTML  

    We address stability of state feedback switched linear systems in which delays are present in both the feedback state and the switching signal of the switched controller. For switched systems with average dwell-time switching signals, we provide a condition, in terms of upper bounds on the delays and in terms of a lower bound on the average dwell-time, to guarantee asymptotic stability of the closed loop. The condition also implies that, in general, feedback switched linear systems are robust with respect to both small state delays and small switching delays. Our approach combines existing multiple Lyapunov function techniques with the merging switching signal technique, which gives relationships between the average dwell times of two mismatched switching signals and their mismatched times. A methodology for numerical solution based on linear matrix inequality is also included. View full abstract»

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  • Bearings-Only Guidance of a Unicycle-Like Vehicle Following a Moving Target With a Smaller Minimum Turning Radius

    Page(s): 2390 - 2395
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (463 KB) |  | HTML iconHTML  

    This technical note addresses the problem of following a moving target by a unicycle-like vehicle. The target may have higher maneuverability and a smaller minimum turning radius than the pursuing vehicle. The goal is to keep the unicycle-like vehicle as close as possible to the target all the time. We present a simple and constructive bearings-only guidance law and give its mathematically rigorous analysis. View full abstract»

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  • Consensus of Multi-Agent Systems With Unbounded Time-Varying Delays

    Page(s): 2396 - 2401
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (329 KB) |  | HTML iconHTML  

    In this note, the consensus problem with infinite time-varying delays for linearly coupled static network is investigated. The delay affects only the off-diagonal terms in continuous-time equations. At first, we define an effective consensus ability index. Then, by using the graph theory and a new concept of consensus, we prove that under some mild conditions, the network can realize consensus. An example is given to show the validity of obtained results. View full abstract»

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  • Manufacturing Systems With a Production Dependent Failure Rate: Structure of Optimality

    Page(s): 2401 - 2406
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (258 KB) |  | HTML iconHTML  

    This technical note provides the structure of a policy minimizing a long term, average, expected, backlog/inventory cost for a fluid model, single machine, single product manufacturing system subject to a failure/repair Markov process, where the failure rate is a piecewise constant function of the production rate. This policy generalizes previous results and confirms several conjectures reported in the literature, providing an interesting insight into the problem. View full abstract»

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Aims & Scope

In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering.  Two types of contributions are regularly considered

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Meet Our Editors

Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame