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Automatic Control, IEEE Transactions on

Issue 9 • Date Sept. 2001

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Displaying Results 1 - 25 of 27
  • Comments on "A revisit to the gain and phase margins of linear quadratic regulators" [with reply]

    Page(s): 1508 - 1509
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (39 KB)  

    In the above paper by Zhang and Fu (ibid. vol.41 (1996)), an example is given showing that the LQ controller gives an arbitrary small gain margin with respect to variations of the open-loop plant. As a remedy, a dynamic-state feedback is proposed which is claimed to give an arbitrary large gain margin. This is incorrect. In fact, the proposed dynamic state feedback controller does not even stabilize the nominal system. In reply, Zhang and Fu show how the error can easily be fixed by modifying the controller concerned, and point out out that the modified controller has the same features as the original one. View full abstract»

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  • A course in robust control theory: a convex approach [Book Reviews]

    Page(s): 1510 - 1511
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    Freely Available from IEEE
  • A geometric approach to fault detection and isolation for bilinear systems

    Page(s): 1451 - 1455
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (176 KB) |  | HTML iconHTML  

    In this paper, a geometric approach to the synthesis of a residual generator for fault detection and isolation (FDI) in bilinear systems is considered. A necessary and sufficient condition to solve the so-called fundamental problem of residual generation is obtained. The proposed approach resorts to extensions of the notions of (C, A)-invariant and unobservability subspaces, and it yields a constructive design method View full abstract»

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  • Production and maintenance control for manufacturing systems

    Page(s): 1455 - 1460
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (208 KB)  

    This paper addresses the production and maintenance control problem of a failure prone manufacturing system consisting of one machine and producing one part type. The machine is assumed to have three working states: good, average and bad, and a failure state. In the three working states, the machine can produce parts and some of these parts are rejected with a rate depending on the machine state. In the failure state, no part is produced. The state transition of the machine is governed by a continuous-time Markov process. The jump rates from average and bad states to the good state are the preventive maintenance rates and the one from failure state to good state is the corrective maintenance rate. The production rate and the maintenance rates are optimized View full abstract»

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  • Decomposition of the supervisory control problem for Petri nets under preservation of maximal permissiveness

    Page(s): 1490 - 1496
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (312 KB) |  | HTML iconHTML  

    Decomposing the design of supervisory control laws for Petri nets is an efficient way to tackle its complexity. We consider legal sets which are the union of two sets. In general, this can make the control law obtained via decomposition too restrictive, i.e., it disables more transitions than necessary. Generalizing existing results, we give structural conditions under which the control law via decomposition is maximally permissive View full abstract»

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  • Sequential control of trace processes

    Page(s): 1496 - 1500
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (192 KB) |  | HTML iconHTML  

    A sequential extension of the Smedingas trace process (TP) control theory is proposed. In this framework, discrete event processes are specified by their behavior traces, independently of any modeled internal dynamics. Controllable maximal sublanguage and minimal superlanguage relative to a given specification language are identified. It is shown that controllers for simultaneous transient and steady-state behaviors can be synthesised in a very intuitive way for a large class of TPs. The theory is exemplified using nonregular processes View full abstract»

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  • On robust stability of time-delay systems with norm-bounded uncertainty

    Page(s): 1426 - 1431
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB) |  | HTML iconHTML  

    This paper considers the robust stability problem for a class of time-delay systems with norm-bounded, and possibly time-varying uncertainty. Based on the discretized Lyapunov functional approach, a stability criterion is derived. The time-delay is assumed constant and known. Numerical examples show that the results obtained by this new criterion significantly improve the estimate of the stability limit over some existing results in the literature View full abstract»

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  • Normalized H controller reduction with a priori error bounds

    Page(s): 1477 - 1483
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    This paper describes an approach to the reduction of controllers for the normalized coprime factor robustness problem as well as the normalized H problem. It is shown that a relative error approximation of a coprime factor representation of any suboptimal controller leads to a stability guarantee and an upper bound on the performance degradation when the reduced order controller is implemented. When the approximation is performed on the controller generator, guaranteed a priori stability and performance bounds are obtained in terms of the synthesis Riccati equation solutions of the normalized H control problems View full abstract»

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  • An adaptive H tracking control for a class of nonlinear multiple-input multiple-output (MIMO) systems

    Page(s): 1432 - 1437
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (256 KB)  

    An adaptive H tracking control equipped with a VSC algorithm is proposed for a class of nonlinear multiple-input-multiple-output (MIMO) systems that are represented by input-output models involving parametric uncertainties, unmodeled perturbations and external disturbances. In order to counteract the effect due to the unmodeled perturbation in the input weighting gain the H tracking control requires to solve a modified algebraic Riccati-like matrix equation. The derived hybrid adaptive-robust tracking control schemes guarantee that all the signals and states are bounded, the tracking error is uniformly and ultimately bounded and an H tracking performance is achieved. Compared with the conventional H tracking control design the developed adaptive-robust H tracking control scheme can be applied to a broader class of nonlinear MIMO systems in the presence of high-degree uncertainties View full abstract»

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  • A primal-dual semi-definite programming approach to linear quadratic control

    Page(s): 1442 - 1447
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (192 KB) |  | HTML iconHTML  

    We study a deterministic linear-quadratic (LQ) control problem over an infinite horizon, without the restriction that the control cost matrix R or the state cost matrix Q be positive-definite. We develop a general approach to the problem based on semi-definite programming (SDP) and related duality analysis. We show that the complementary duality condition of the SDP is necessary and sufficient for the existence of an optimal LQ control under a certain stability condition (which is satisfied automatically when Q is positive-definite). When the complementary duality does hold, an optimal state feedback control is constructed explicitly in terms of the solution to the primal SDP View full abstract»

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  • An improved version of the singularity-induced bifurcation theorem

    Page(s): 1483 - 1486
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (176 KB) |  | HTML iconHTML  

    It has been shown recently that there is a new type of codimension one bifurcation, called the singularity-induced bifurcation (SIB), arising in parameter dependent differential-algebraic equations (DAEs) of the form x˙=f and 0=g, and which occurs generically when an equilibrium path of the DAE crosses the singular surface defined by g=0 and det gy=0. The SIB refers to a stability change of the DAE owing to some eigenvalue of a related linearization diverging to infinity when the Jacobian gy is singular. In this article an improved version (Theorem 1.1) of the SIB theorem with its simple proof is given, based on a decomposition theorem (Theorem 2.1) of parameter dependent polynomials View full abstract»

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  • Passive velocity field control (PVFC). Part II. Application to contour following

    Page(s): 1360 - 1371
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (360 KB) |  | HTML iconHTML  

    When the contour following task is represented by a velocity field on the configuration manifold of the system, the coordination aspect of the problem is made explicit. The PVFC scheme developed in the Part I (ibid. vol.29(9) (2001)) can then be applied to track the defined velocity field. However, for some contours, an encoding velocity held on the configuration manifold does not exist or is difficult to define and, as a consequence, the PVFC cannot be directly applied. For systems whose configuration manifolds are compact Lie groups and the desired contour is represented by a parameterized trajectory, a general methodology is developed, using a suspension technique, to define a velocity field on a manifold related to the configuration manifold of the system for which PVFC can be applied. With this strategy, timing along the contour can be naturally varied online by a self-pacing scheme so that the contour tracking performance can be improved. The experimental results for a 2-DOF robot following a Lissajous contour illustrates and verifies the convergence and robustness properties of the PVFC methodology View full abstract»

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  • Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence

    Page(s): 1447 - 1451
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (176 KB) |  | HTML iconHTML  

    An universal controller is constructed, formulated in input-output terms only, which causes the output of any uncertain smooth single-input single-output (SISO) minimum-phase dynamic system with known relative degree to vanish in finite time. This allows exact tracking of arbitrary real-time smooth signals. Only one parameter is to be adjusted. Since the approach is based on higher order finite time-convergence sliding modes, the control can be made arbitrarily smooth, providing for the arbitrarily-high tracking-accuracy order with respect to the sampling step View full abstract»

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  • A new bounded real lemma representation for the continuous-time case

    Page(s): 1420 - 1426
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB) |  | HTML iconHTML  

    A differential linear matrix inequality (DLMI) approach is introduced for the solution of various linear continuous-time control problems. The proposed method permits the application of linear matrix inequalities (LMIs) to the solution of control design problems under uncertainty. These problems are solved for finite horizon linear systems while considerably reducing the overdesign inherent in previous methods. The new approach also allows for the solution of the output-feedback control problem for systems belonging to a finite set of uncertain plants with hardly any overdesign. Four examples are given to demonstrate the applicability of the new method View full abstract»

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  • Numerical solutions to the Witsenhausen counterexample by approximating networks

    Page(s): 1471 - 1477
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (304 KB)  

    Approximate solutions to the Witsenhausen counterexample (1968) are derived by constraining the unknown control functions to take on fixed structures containing “free” parameters to be optimized. Such structures are given by “nonlinear approximating networks”, i.e., linear combinations of parametrized basis functions that benefit by density properties in normed linear spaces. This reduces the original functional problem to a nonlinear programming one which is solved via stochastic approximation. The method yields lower values of the costs than the ones achieved so far in the literature, and, most of all, provides rather a complete overview of the shapes of the optimal control functions when the two parameters that characterize the Witsenhausen counterexample vary. One-hidden-layer neural networks are chosen as approximating networks View full abstract»

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  • Stabilization of nonlinear systems via designed center manifold

    Page(s): 1372 - 1383
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (344 KB)  

    This paper addresses the problem of local state feedback stabilization of a class of nonlinear systems with nonminimum phase zero dynamics. A new technique, namely, the Lyapunov function with homogeneous derivative along solution curves was developed to test the approximate stability of the dynamics on the center manifold. A set of convenient sufficient conditions are provided to test the negativity of the homogeneous derivatives. Using these conditions and assuming the zero dynamics has stable and center linear parts, a method is proposed to design controls such that the dynamics on the designed center manifold of the closed-loop system is approximately stable. It is proved that using this method, the first variables in each of the integral chains of the linearized part of the system do not affect the approximation order of the dynamics on the center manifold. Based on this fact, the concept of injection degree is proposed. According to different kinds of injection degrees certain sufficient conditions are obtained for the stabilizability of the nonminimum phase zero dynamics. Corresponding formulas are presented for the design of controls View full abstract»

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  • Reachability and controllability of switched linear discrete-time systems

    Page(s): 1437 - 1441
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    This paper investigates the reachability and controllability issues for switched linear discrete-time systems. Geometric characterization of controllability is presented. For reversible systems, the controllable sets and the reachable sets are identified in Wonham's geometric approach, and verifiable conditions for reachability and controllability are also presented View full abstract»

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  • Fundamental limits in sensitivity minimization: multiple-input-multiple-output (MIMO) plants

    Page(s): 1486 - 1489
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (216 KB) |  | HTML iconHTML  

    This paper provides a bridge between the H literature and that of fundamental limits. By applying operator theoretic tools developed for the standard frequency domain, model-matching approach to sensitivity minimization, explicit closed form expressions are given for tight bounds on the H norm of weighted sensitivity functions for output feedback control of linear multivariable systems View full abstract»

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  • Passive velocity field control (PVFC). Part I. Geometry and robustness

    Page(s): 1346 - 1359
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (392 KB)  

    Passive velocity field control is a control methodology for fully actuated mechanical systems, in which the motion task is specified behaviorally in terms of a velocity field, and the closed-loop system is passive with respect to a supply rate given by the environment power input. The control law is derived geometrically and the geometric and robustness properties of the closed-loop system are analyzed. It is shown that the closed-loop unforced trajectories are geodesics of a closed-loop connection which is compatible with an inertia metric, and that the velocity of the system converges exponentially to a scaled multiple of the desired velocity field. The robustness property of the system exhibits some strong directional preference. In particular, disturbances that push in the direction of the desired momentum do not adversely affect the performance. Moreover, robustness property also improves with more energy in the system View full abstract»

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  • Identification of stable models in subspace identification by using regularization

    Page(s): 1416 - 1420
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB) |  | HTML iconHTML  

    In subspace identification methods, the system matrices are usually estimated by least squares, based on estimated Kalman filter state sequences and the observed inputs and outputs. For a finite number of data points, the estimated system matrix is not guaranteed to be stable, even when the true linear system is known to be stable. In this paper, stability is imposed by using regularization. The regularization term used here is the trace of a matrix which involves the dynamical system matrix and a positive (semi) definite weighting matrix. The amount of regularization can be determined from a generalized eigenvalue problem. The data augmentation method of Chui and Maciejowski (1996) is obtained by using specific choices for the weighting matrix in the regularization term View full abstract»

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  • Stabilization of linear systems with limited information

    Page(s): 1384 - 1400
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (368 KB) |  | HTML iconHTML  

    We show that the coarsest, or least dense, quantizer that quadratically stabilizes a single input linear discrete time invariant system is logarithmic, and can be computed by solving a special linear quadratic regulator problem. We provide a closed form for the optimal logarithmic base exclusively in terms of the unstable eigenvalues of the system. We show how to design quantized state-feedback controllers, and quantized state estimators. This leads to the design of hybrid output feedback controllers. The theory is then extended to sampling and quantization of continuous time linear systems sampled at constant time intervals. We generalize the definition of density of quantization to the density of sampling and quantization in a natural way, and search for the coarsest sampling and quantization scheme that ensures stability. Finally, by relaxing the definition of quadratic stability, we show how to construct logarithmic quantizers with only finite number of quantization levels and still achieve practical stability of the closed-loop system View full abstract»

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  • Further results on variable output feedback controllers

    Page(s): 1505 - 1508
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (128 KB) |  | HTML iconHTML  

    Zak and Hui (1993) proposed a sliding mode controller for linear multiple-input-multiple-output (MIMO) systems using static output feedback. The author's previous paper (1996) provides an improvement of the output feedback controller of Zak-Hui for a class of linear single-input-single-output (SISO) systems that eliminated two important limitations: 1) system uncertainties must be bounded by the system output; and 2) a requirement of a matrix inequality. The controller developed previously can guarantee global closed-loop stability. This paper extends the previous results to linear MIMO systems. It is emphasized that the proposed MIMO controller yields global closed-loop stability whereas the one in Zak-Hui can only guarantee local stability. An application of the proposed MIMO controller to an aircraft model is included to show the effectiveness of the method View full abstract»

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  • Per-queue stability analysis of a random access system

    Page(s): 1466 - 1470
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (168 KB) |  | HTML iconHTML  

    We have extended our previous studies (2000) of the system stability of buffered ALOHA systems to study an individual queue's stability, i.e., per-queue stability. The main result obtained in this work is a necessary and sufficient per-queue stability condition, which can be computed analytically only for several cases. For other incomputable cases, we evaluated several inner and outer bounds. They are generally quite tight for not-so-asymmetric systems View full abstract»

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  • Stabilization of nonlinear systems via forwarding mod {LgV}

    Page(s): 1461 - 1466
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (192 KB)  

    Forwarding is a tool for constructing stabilizers for nonlinear systems. A key step in this design technique is to find an explicit solution to a partial differential equation (PDE), which may be hard to find (actually, the PDE may even not be solvable at all). In this paper we show that it is possible to provide an additional degree of freedom for the solution of the aforementioned PDE, hence effectively extending the realm of application of the forwarding methodology. Our contribution is illustrated with the example of an inverted pendulum with a disk inertia View full abstract»

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  • Exploiting symmetry in the synthesis of supervisors for discrete event systems

    Page(s): 1500 - 1505
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB) |  | HTML iconHTML  

    We investigate a method to exploit the symmetry inherent to many discrete-event systems in order to reduce the computational complexity of the supervisory control problem (SCP). We characterize symmetry using notions of group theory and derive conditions under which there exists a quotient (reduced) automaton representation for a language with, in general, a much smaller state space than the original minimal (in number of states) automaton representation for the language. We then propose an algorithm to synthesize a solution to the SCP which is similar to the classical one, but performed on reduced automata. Special attention is given to the particular case of systems whose models contain similar components. The approach is illustrated by an example of control of a small production line 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