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Automatic Control, IEEE Transactions on

Issue 10 • Date Oct. 1998

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Displaying Results 1 - 25 of 26
  • Comments on "A procedure for the positive definiteness of forms of even order"

    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (39 KB)  

    Hasan and Hasan (IEEE Trans. Automat. Control., Vol.41, p.615-17, 1996) give a necessary and sufficient condition for the positive definiteness of a quadratic programming problem. The purpose of this paper is to point out that the main result in the above-mentioned paper by is erroneous. View full abstract»

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  • On the use of compensated total least squares in system identification

    Page(s): 1436 - 1441
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (243 KB)  

    A bias-compensated total least squares estimator is proposed for models which are linear-in-the-parameters and nonlinear in the perturbed input and output signals. The estimates are obtained using a noniterative and numerically stable method. Strong consistency of both the generalized total least squares and the compensated total least squares estimates are proven. The theoretical properties are verified through simulations. View full abstract»

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  • Identification of linear systems via spectral analysis given time-domain data: consistency, reduced-order approximation, and performance analysis

    Page(s): 1354 - 1373
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (912 KB)  

    Estimation of a parametric input-output (I/O) infinite impulse response transfer function given time-domain I/O data is considered. Some of the desirable properties of any approach to this problem are: unimodality of the performance surface, consistent identification in the sufficient-order case, and stability of the fitted model under undermodeling. We first consider a frequency-domain solution to the least squares equation error identification problem using the power spectrum and the cross-spectrum of the I/O data to estimate the I/O parametric transfer function. The proposed approach is shown to yield a unimodal performance surface, consistent identification in colored noise and sufficient-order case, and stable fitted models under undermodeling for arbitrary stationary inputs so long as they are persistently exciting of sufficiently high order. Asymptotic performance analysis is carried out for both sufficient-order and reduced-order cases. These asymptotic results are then used to derive statistics on the corresponding estimated transfer function. We also investigate an iterative pseudomaximum likelihood approach and analyze its performance under sufficient-order modeling. Finally, computer simulation examples are provided to illustrate the two approaches View full abstract»

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  • An exact solution to general four-block discrete-time mixed ℋ 2/ℋ problems via convex optimization

    Page(s): 1475 - 1480
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB)  

    The mixed ℋ2 control problem can be motivated as a nominal LQG optimal control problem subject to robust stability constraints, expressed in the form of an ℋ norm bound. This paper contains a solution to a general four-block mixed ℋ2/ℋ problem, based upon constructing a family of approximating problems. Each one of these problems consists of a finite-dimensional convex optimization and an unconstrained standard ℋ problem. The set of solutions is such that in the limit the performance of the optimal controller is recovered, allowing one to establish the existence of an optimal solution. Although the optimal controller is not necessarily finite-dimensional, it is shown that a performance arbitrarily close to the optimal can be achieved with rational controllers. Moreover, the computation of a controller yielding a performance ε-away from optimal requires the solution of a single optimization problem, a task that can be accomplished in polynomial time View full abstract»

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  • Robust right coprime factorization and robust stabilization of nonlinear feedback control systems

    Page(s): 1505 - 1509
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    Robust right coprime factorization and robust stabilization of nonlinear feedback control systems are studied. The concept of robust right coprime factorization of nonlinear operators for feedback control systems is introduced. Some conditions for the robustness of a right coprime factorization of a nonlinear plant under unknown but bounded perturbations are derived. An example with a closed-form solution is included to illustrate the general theory and a step-by-step construction of the robust factorization and the robust stabilization View full abstract»

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  • Mean square stochastic stability of linear time-delay system with Markovian jumping parameters

    Page(s): 1456 - 1460
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    This paper deals with the mean square stochastic stability of the class of linear time-delay systems with Markovian jumping parameters. A delay-independent sufficient condition for checking the stochastic stability of this class of systems is established. A numerical example is given to show the usefulness of the proposed theoretical results View full abstract»

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  • Global adaptive output feedback stabilization of nonlinear systems of any relative degree with unknown high-frequency gains

    Page(s): 1442 - 1446
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (228 KB)  

    This paper presents an algorithm for adaptive output feedback stabilization of nonlinear single-input/single-output, minimum phase systems of any relative degree which are linear with respect to input and unknown constant parameter vector. The algorithm does not require the knowledge of the sign of the high-frequency gain View full abstract»

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  • On the thirty-two virtual polynomials to stabilize an interval plant

    Page(s): 1460 - 1465
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    This paper studies the conservatism of the 32 virtual polynomials to stabilize an interval plant. It is shown that working with the 32 virtual vertices is generally less conservative than with the Kharitonov polynomials of the smallest interval polynomial containing the characteristic polynomial polytope. By means of the former, it is possible to find all the controllers such that the value set of the polytope of characteristic polynomials is applied in two quadrants as a maximum for each ω; while using the latter, only some of them can be found. The cases in which both methods coincide are also analyzed, and the conditions on the numerator and denominator of the controller are developed. Thus, this coincidence can be known a priori from the characteristics of the coefficients of the numerator and denominator of the controller. It is shown that these conditions are satisfied by the first-order controllers View full abstract»

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  • MIMO optimal control design: the interplay between the ℋ2 and the l1 norms

    Page(s): 1374 - 1388
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    We consider controller design methods which can address directly the interplay between the ℋ2 and l1 performance of the closed loop. The development is devoted to multi-input/multi-output (MIMO) systems. Two relevant multi-objective performance problems are considered each being of interest in its own right. In the first, termed as the combination problem, a weighted sum of the l1 norms and the square of the ℋ2 norms of a given set of input-output transfer functions constituting the closed loop is minimized. It is shown that, in the one-block case, the solution can be obtained via a finite-dimensional quadratic optimization problem which has an a priori known dimension. In the four-block case, a method of computing approximate solutions within any a priori given tolerance is provided. In the second, termed as the mixed problem, the ℋ2 performance of the closed loop is minimized subject to an l1 constraint. It is shown that approximating solutions within any a priori given tolerance can be obtained via the solution to a related combination problem View full abstract»

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  • Static output feedback stabilization with prescribed degree of stability

    Page(s): 1493 - 1496
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (132 KB)  

    The problem of finding a static output feedback matrix is restated. The new formulation replaces the solution of a set of inversely coupled Lyapunov inequalities with the simultaneous solution to an algebraic Riccati inequality and a Lyapunov inequality. An algorithm is developed based on the restated problem. Unlike previous algorithms, the algorithm is noniterative in linear matrix inequality (LMI) solutions. The algorithm may be used to prescribe a given degree of stability, while keeping the static output feedback gain small. Use of the algorithm is demonstrated via an example View full abstract»

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  • A general approach to input-output pseudolinearization for nonlinear systems

    Page(s): 1497 - 1501
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (200 KB)  

    A nonlinear system is said to be input-output pseudolinearized if its family of linearizations about constant operating points has input-output behavior that is independent of the particular operating point. The problem of constructing static state feedback laws that achieve input-output pseudolinearization for a general class of nonlinear systems is considered. A generalization of the well-known structure algorithm to the case of parameterized families of linear systems plays an important role View full abstract»

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  • Multivariable pi-sharing theory and its application on the Lur'e problem

    Page(s): 1501 - 1505
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (184 KB)  

    The pi-sharing theory developed by Lawrence and Johnson (1986) is extended to handle square multivariable continuous-time systems, and for the most essential part of finding usable pi-coefficients, LMI formulations are utilized such that for any finite-dimensional LTI systems, time-invariant pi-coefficients can be obtained easily. Furthermore, pi-coefficients are derived for sector-bounded nonlinearities, and the extended pi-sharing theory is applied to the multivariable Lur'e problem. With this approach, not only can a Lur'e system with known sector bounds on nonlinearities be checked for stability, but also the maximal bounds ensuring stability can be found under some conditions View full abstract»

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  • Global approximate output tracking for nonlinear systems

    Page(s): 1389 - 1398
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    Addresses the global output tracking problem for nonlinear systems with singular points. For nonlinear systems which satisfy a suitable observability condition, the authors identify a class of smooth output trajectories which the system can track using continuous open-loop controls. This class includes all output trajectories generated by smooth state feedback. They then study the problem of approximate output tracking using discontinuous time-varying feedback controllers. Given a smooth output trajectory for which exact tracking is possible, the authors construct a discontinuous feedback controller which achieves robust tracking of the desired output trajectory in the face of perturbations. Finally, it is shown that their results can be applied to the control of a chain system, and some numerical results are presented to illustrate the performance of their controller View full abstract»

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  • Formulas for the extremal controllable sequences in timed-event graphs

    Page(s): 1465 - 1468
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    This paper studies controllable sequences in the max-algebra model of timed event graphs. We present a formula for the supremal controllable sequence when a desirable behavior is specified as a single sequence. As a result, the supremal sequence can be computed without iterative computation. A formula for the infimal controllable sequence is also obtained under some assumptions View full abstract»

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  • Markov decision processes and regular events

    Page(s): 1399 - 1418
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    Desirable properties of the infinite histories of a finite-state Markov decision process are specified in terms of a finite number of events represented as ω-regular sets. An infinite history of the process produces a reward which depends on the properties it satisfies. The authors investigate the existence of optimal policies and provide algorithms for the construction of such policies View full abstract»

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  • Continuous-time Wiener system identification

    Page(s): 1488 - 1493
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    A continuous-time Wiener system is identified. The system consists of a linear dynamic subsystem and a memoryless nonlinear one connected in a cascade. The input signal is a stationary white Gaussian random process. The system is disturbed by stationary white random Gaussian noise. Both subsystems are identified from input-output observations taken at the input and output of the whole system. The a priori information is very small and, therefore, resulting identification problems are nonparametric. The impulse impulse of the linear part is recovered by a correlation method, while the nonlinear characteristic is estimated with the help of the nonparametric kernel regression method. The authors prove convergence of the proposed identification algorithms and examine their convergence rates View full abstract»

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  • Global regulation of elastic joint robots based on energy shaping

    Page(s): 1451 - 1456
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    The energy-shaping methodology introduced by Takegaki and Arimoto (1981) is a powerful tool for global regulator design for rigid robot manipulators. In this paper we extend this approach to the global regulator design for elastic joint robots. Under this framework we broach the cases when rotor positions and velocities are available for measurement as well as when only rotor positions can be measured. The structure of these regulators is given by the gradient of a suitable class of artificial potential energies and damping injection via rotor velocity or an appropriate filtering of rotor position View full abstract»

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  • New finite-dimensional risk-sensitive filters: small noise limits

    Page(s): 1424 - 1429
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    The paper is concerned with continuous-time nonlinear risk-sensitive filters. It is shown that for large classes of nonlinearities entering both the dynamics and measurements, these filters are finite-dimensional generalizations of the Benes filters. Specific examples are discussed. The small noise limiting analog is discussed using change of probability measures View full abstract»

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  • On the use of compensated total least squares in system identification

    Page(s): 1436 - 1441
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (248 KB)  

    A bias-compensated total least squares estimator is proposed for models which are linear-in-the-parameters and nonlinear in the perturbed input and output signals. The estimates are obtained using a noniterative and numerically stable method. Strong consistency of both the generalized total least squares and the compensated total least squares estimates are proven. The theoretical properties are verified through simulations View full abstract»

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  • Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

    Page(s): 1480 - 1484
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (188 KB)  

    The simultaneous perturbation stochastic approximation (SPSA) algorithm has attracted considerable attention for challenging optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo process. The objective is to minimize the mean square error of the estimate. The authors also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector is found to be a symmetric Bernoulli in both cases. The authors end the paper with a numerical study related to the area of experiment design View full abstract»

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  • Net structure and control logic synthesis of controlled Petri nets

    Page(s): 1446 - 1450
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (216 KB)  

    Control logic synthesis of discrete-event systems is considered in the setting of controlled Petri nets. The problem is to find a control policy that restricts the behavior of a controlled Petri net so that a collection of forbidden state conditions is satisfied. S-decreases are introduced as a tool for the control synthesis. The S-decreases are weight vectors defined on the places of a net such that the weighted sum of tokens in the net never increases with any transition firing. On the basis of S-decreases, the authors propose an efficient method for the synthesis of the maximally permissive state feedback control polity for a class of controlled Petri nets whose uncontrolled subnets are forward and backward conflict-free nets. This method upgrades all integer linear programming-based methods for which one only requires to solve the much simpler linear programming problems to determine maximally permissive controls View full abstract»

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  • Feedback stabilization of some event graph models

    Page(s): 1419 - 1423
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (124 KB)  

    The authors introduce several notions of stability for event graph models, timed or not. The stability is similar to the boundedness notion for Petri nets. The event graph models can be controlled by an output feedback which takes information from some observable transitions and can disable some controllable transitions. The controller itself is composed of an event graph. In this framework the authors solve the corresponding stabilization problems, i.e., they wonder if such a controller may prevent the explosion of the number of tokens View full abstract»

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  • Optimal feedback control strategies for state-space systems with stochastic parameters

    Page(s): 1469 - 1475
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    Two different optimal feedback laws are derived for state-space systems parametrized through an independent identically distributed vector sequence. Both feedback laws are obtained by minimizing the expectation of a multistep quadratic loss function at each time step. They differ on the assumptions made about the future inputs. The properties and implementability of the feedback laws are discussed for the infinite horizon case View full abstract»

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