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Automatic Control, IEEE Transactions on

Issue 4 • Date April 1996

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Displaying Results 1 - 22 of 22
  • Optimal control of perturbed linear static systems

    Publication Year: 1996 , Page(s): 579 - 584
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3479 KB)  

    This paper considers the problem of designing an optimal controller for a linear static system with uncertainty modeled as a single induced Euclidean norm bounded multi-input-multi-output (MIMO) perturbation. The objective is the minimization of the singular value of the disturbance to error transfer function. The static (constant matrix) design problem is convex and can be formulated as a sequence of generalized eigenvalue problems. We present a detailed example, applying the approach to the steady-state control of the temperature distribution over a radiantly heated two-dimensional plate. View full abstract»

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  • Comments Regarding "Comments on 'Modified Extended Kalman Filtering and a Real-Time Parallel Algorit

    Publication Year: 1996
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (129 KB)  

    First Page of the Article
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  • Direct Adaptive Control Algorithms: Theory and Applications [Book Reviews]

    Publication Year: 1996
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    Freely Available from IEEE
  • Periodic and chaotic dynamics of a switched-server system under corridor policies

    Publication Year: 1996 , Page(s): 584 - 588
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (540 KB)  

    We consider a fluid model of a manufacturing system serving three buffers (part-types). The system operates under a feedback control policy called a corridor policy. This policy determines the times to switch between buffers and to which buffers to switch. The machine is assumed to be perfectly flexible, i.e., the switching times between buffers are zero. Open and closed versions of the system are considered. We give two sets of conditions on the parameters of the corridor: one guarantees periodic dynamics and the other chaotic behavior View full abstract»

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  • Bilinear transformation and generalized singular perturbation model reduction

    Publication Year: 1996 , Page(s): 589 - 593
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (456 KB)  

    A new general bilinear relationship is found between continuous and discrete generalized singular perturbation reduced-order models. This result is applied to the problem of deriving discrete analogs of continuous singular perturbation and direct truncation model reduction and leads to a new definition of discrete “Nyquist” model reduction. Also, “unit circle” bilinear transformations are used to relate several known facts about continuous and discrete balanced model reduction and incorporate them into a symmetrical, unified framework View full abstract»

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  • Mean-square stabilizing solutions for discrete-time coupled algebraic Riccati equations

    Publication Year: 1996 , Page(s): 593 - 598
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (624 KB)  

    In this paper we present new sufficient conditions for the existence of a mean-square stabilizing solution for a set of coupled algebraic Riccati equations which arises from the study of quadratic optimal control of discrete-time linear systems with Markov switching parameters. The conditions are derived under the assumptions of mean-square stabilizability and on the unobservable modes of the system and compared with existing results View full abstract»

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  • Periodic output feedback stabilization of neutral systems

    Publication Year: 1996 , Page(s): 511 - 521
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1000 KB)  

    A new feedback control technique called periodic output feedback is investigated in the context of infinite-dimensional linear systems modeled by neutral functional differential equations. In this method, discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control. This work focuses on stabilization of neutral systems with delayed control modeled in the state space W2(1) ([-r,0];Rn)×L 2([-r,0],Rp), where W2(1)([-r,0];Rn) denotes the Sobolev space of Rn-valued, absolutely continuous functions with square integrable derivatives on [-r,0]. We show that a class of these systems can be stabilized by periodic output feedback, even though their input operators are unbounded. We overcome this difficulty by representing the system state using an abstract integral “variation of constants” formula. An algorithm is presented at the end of this paper to construct a periodic output feedback gain function. An example is provided to illustrate the construction of the gain function View full abstract»

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  • Numerical differentiation and parameter estimation in higher-order linear stochastic systems

    Publication Year: 1996 , Page(s): 522 - 532
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (756 KB)  

    For a linear time-invariant system of order d⩾2 with a white noise disturbance, the input and the output are assumed to be sampled at regular time intervals. Using only these observations, some approximate values of the first d-1 derivatives are obtained by a numerical differentiation scheme, and the unknown system parameters are estimated by a discretization of the continuous-time least-squares formulas. These parameter estimates have an error which does not approach zero as the sampling interval approaches zero. This asymptotic error is shown to be associated with the inconsistency of the quadratic variation estimate of the white noise local variance based on the sampled observations. The use of an explicit correction term in the least-squares estimates or the use of some special numerical differentiation formulas eliminates the error in the estimates View full abstract»

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  • A simple procedure for the stabilization of a class of uncontrollable generalized systems

    Publication Year: 1996 , Page(s): 603 - 607
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (432 KB)  

    This paper gives a simple procedure for the stabilization, with a prescribed rate of convergence of the free motions, of a class of (possibly, single-input) uncontrollable generalized continuous-time time-invariant linear systems, preserving the impulse-free property (if any) View full abstract»

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  • On the solution to the Sylvester matrix equation AV+BW=EVF

    Publication Year: 1996 , Page(s): 612 - 614
    Cited by:  Papers (51)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (244 KB)  

    A simple, direct, complete and explicit parametric solution of the generalized Sylvester matrix equation AV+BW=EVF is proposed for matrix F in the Jordan form with arbitrary eigenvalues using the Smith canonical form of the matrix [A-sE B]. The obtained solution is in a clear, neat form and may have important applications in descriptor linear system theory View full abstract»

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  • Learning by canonical smooth estimation. II. Learning and choice of model complexity

    Publication Year: 1996 , Page(s): 557 - 569
    Cited by:  Papers (16)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1192 KB)  

    This paper analyzes the properties of a procedure for learning from examples. This “canonical learner” is based on a canonical error estimator developed in Part I. In learning problems one can observe data that consists of labeled sample points, and the goal is to find a model or “hypothesis” from a set of candidates that will accurately predict the labels of new sample points. The expected mismatch between a hypothesis prediction and the actual label of a new sample point is called the hypothesis “generalization error”. We compare the canonical learner with the traditional technique of finding hypotheses that minimize the relative frequency-based empirical error estimate. It is shown that for a broad class of learning problems, the set of cases for which such empirical error minimization works is a proper subset of the cases for which the canonical learner works. We derive bounds to show that the number of samples required by these two methods is comparable. We also address the issue of how to determine the appropriate complexity for the class of candidate hypotheses View full abstract»

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  • Adaptive control of nonlinear systems via approximate linearization

    Publication Year: 1996 , Page(s): 618 - 625
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (748 KB)  

    This paper presents an adaptive control scheme for nonlinear systems that violates some of the common regularity and structural conditions of current nonlinear adaptive schemes such as involutivity, existence of a well-defined relative degree, and minimum phase property. While the controller is designed using an approximate model with suitable properties, the parameter update law is derived from an observation error based on the exact model described in suitable coordinates. The authors show that this approach results in a stable, closed-loop system and achieves adaptive tracking with bounds on the tracking error and parameter estimates. The authors also present a constructive procedure for adaptive state regulation which is based on the quadratic linearization technique via dynamic state feedback. This regulation scheme does not impose any restriction on the location of the unknown parameters and is applicable to any linearly controllable nonlinear system View full abstract»

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  • Corrections to “Finite buffer realization of input-output discrete event systems”

    Publication Year: 1996 , Page(s): 625 - 627
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (204 KB)  

    This paper presents a correction to theorem 4 in the above paper by the authors (see ibid., vol.40, no.6, p.1042-53, 1995) which provides a necessary and sufficient condition for dispatchability View full abstract»

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  • New algebraic-geometric conditions for the linearization by input-output injection

    Publication Year: 1996 , Page(s): 598 - 603
    Cited by:  Papers (52)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (540 KB)  

    The goal of this paper is twofold. It unifies and generalizes existing results on input-output injection linearization of nonlinear systems. The problem is solved as a realization problem since it is based on the analysis of the structure of the input-output differential equation. The necessary and sufficient conditions are derived from a simplified and constructive procedure. For clarity, the paper is limited to the case of single output systems. Exterior differential systems are extensively used throughout the paper, giving constructive conditions View full abstract»

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  • Optimization of the l-induced norm under full state feedback

    Publication Year: 1996 , Page(s): 533 - 544
    Cited by:  Papers (46)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (940 KB)  

    This paper considers the l-optimal control problem, i.e., minimization of the effects of disturbances as measured by the l-induced norm. Earlier work showed that even in the case of full state feedback, optimal and near-optimal linear controllers may be dynamic and of arbitrarily high order. However, previous work by the author derived the existence of near-optimal nonlinear controllers which are static. This paper presents a constructive algorithm for such nonlinear controllers. The main idea is to construct a certain subset of the state space such that achieving disturbance rejection is equivalent to restricting the state dynamics to this set. A construction of this subset requires the solution of several finite, linear programs with the number of variables being at least the number of states but less than the number of states plus the number of controls. The concept of controlled invariance plays a central role throughout View full abstract»

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  • Noncausal inverses for linear systems

    Publication Year: 1996 , Page(s): 608 - 611
    Cited by:  Papers (57)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (416 KB)  

    Suppose we are to guide a plant with a square transfer matrix through a series of way points. This can be accomplished by output tracking of trajectories which are fitted together in a sufficiently smooth manner. Each segment of each output is prescribed in terms of a polynomial or sine function or the product thereof. Our technique is to compute: 1) a noncausal “particular solution” based on the desired trajectory over each segment and the movement from one segment to the next, and this “particular solution” consists of a “particular control” and a “particular state trajectory”; and 2) a regulator to handle modeling errors, disturbances, etc. We concentrate on the “particular solution” View full abstract»

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  • Learning by canonical smooth estimation. I. Simultaneous estimation

    Publication Year: 1996 , Page(s): 545 - 556
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1168 KB)  

    This paper examines the problem of learning from examples in a framework that is based on, but more general than, Valiant's probably approximately correct (PAC) model for learning. In our framework, the learner observes examples that consist of sample points drawn and labeled according to a fixed, unknown probability distribution. Based on this empirical data, the learner must select, from a set of candidate functions, a particular function or “hypothesis” that will accurately predict the labels of future sample points. The expected mismatch between a hypothesis prediction and the label of a new sample point is called the hypothesis “generalization error”. Following the pioneering work of Vapnik and Chervonenkis, others have attacked this sort of learning problem by finding hypotheses that minimize the relative frequency-based empirical error estimate. We generalize this approach by examining the “simultaneous estimation” problem. We demonstrate how one can learn from such a simultaneous error estimate and propose a new class of estimators called “smooth estimators”. We characterize the class of simultaneous estimation problems solvable by a smooth estimator View full abstract»

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  • H-control of discrete-time nonlinear systems

    Publication Year: 1996 , Page(s): 494 - 510
    Cited by:  Papers (61)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1480 KB)  

    This paper presents an explicit solution to the problem of disturbance attenuation with internal stability via full information feedback, state feedback, and dynamic output feedback, respectively, for discrete-time nonlinear systems. The H-control theory is first developed for affine systems and then extended to general nonlinear systems based on the concepts of dissipation inequality, differential game, and LaSalle's invariance principle in discrete time. A substantial difficulty that V(A(x)+B(x)u+E(x)w) [respectively, V(f(x,u,w))] is no longer quadratic in [wu] arising in the case of discrete-time nonlinear systems has been surmounted in the paper. In the case of a linear system, we show how the results reduce to the well-known ones recently proposed in the literature View full abstract»

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  • Smoothing for random fields modeled by partial differential equations

    Publication Year: 1996 , Page(s): 575 - 578
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (304 KB)  

    The authors present an efficient, numerically reliable smoothing algorithm for random fields modeled by linear, constant coefficient, partial differential equations. The estimate is computed from discrete measurements by using the discrete Fourier transform to convert the two-dimensional (2D) problem to a collection of uncoupled one-dimensional (1D) problems which are then solved using stable iterations View full abstract»

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  • A procedure for the positive definiteness of forms of even order

    Publication Year: 1996 , Page(s): 615 - 617
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (256 KB)  

    A positivity method for forms of even order is reported. It is shown that testing for positivity of such forms can be reduced to a test for positive definiteness of parametric-matrices. Special emphasis is placed on quartic- and sixth-order forms. Examples are given to illustrate the proposed criterion View full abstract»

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  • On a quantitative theory of robust adaptive control: an interval plant approach

    Publication Year: 1996 , Page(s): 570 - 574
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (472 KB)  

    This paper considers a robust direct-model reference adaptive control scheme, where the components of the estimated controller parameter vector are constrained to vary in certain prespecified intervals. This interval constraint facilitates the quantitative analysis of the robustness of the closed-loop adaptive control system. Extending existing results from the area of robust parametric stability, a tractable procedure is developed for verifying a condition which guarantees the boundedness of all the closed-loop signals. The robustness verification using this procedure involves the calculation of worst-case “shifted” H norms over certain extremal one-parameter families. This makes the condition easily verifiable, whereas otherwise one is faced with the formidable task of determining the worst-case norms over higher-dimensional compact convex sets in the plant and controller parameter spaces. A simple example is used in the paper to illustrate the theoretical development View full abstract»

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  • Multiple-model estimation with variable structure

    Publication Year: 1996 , Page(s): 478 - 493
    Cited by:  Papers (124)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1600 KB)  

    Existing multiple-model (MM) estimation algorithms have a fixed structure, i.e. they use a fixed set of models. An important fact that has been overlooked for a long time is how the performance of these algorithms depends on the set of models used. Limitations of the fixed structure algorithms are addressed first. In particular, it is shown theoretically that the use of too many models is performance-wise as bad as that of too few models, apart from the increase in computation. This paper then presents theoretical results pertaining to the two ways of overcoming these limitations: select/construct a better set of models and/or use a variable set of models. This is in contrast to the existing efforts of developing better implementable fixed structure estimators. Both the optimal MM estimator and practical suboptimal algorithms with variable structure are presented. A graph-theoretic formulation of multiple-model estimation is also given which leads to a systematic treatment of model-set adaptation and opens up new avenues for the study and design of the MM estimation algorithms. The new approach is illustrated in an example of a nonstationary noise identification problem 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