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Automatic Control, IEEE Transactions on

Issue 1 • Date Jan. 1997

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Displaying Results 1 - 14 of 14
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  • A lower bound for the mixed μ problem

    Page(s): 123 - 128
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    The mixed μ problem has been shown to be NP hard so that exact analysis appears intractable. Our goal then is to exploit the problem structure so as to develop a polynomial time algorithm that approximates μ and usually gives good answers. To this end it is shown that μ is equivalent to a real eigenvalue maximization problem, and a power algorithm is developed to tackle this problem. The algorithm not only provides a lower bound for μ but has the property that μ is (almost) always an equilibrium point of the algorithm View full abstract»

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  • Adaptive nonlinear output feedback tracking with a partial high-gain observer and backstepping

    Page(s): 106 - 113
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    An adaptive output feedback controller for nonlinear systems with nonlinearities depending on the first r (1⩽r⩽n) derivatives of the output is proposed. The derivatives are estimated with a partial state high-gain observer, and the remaining states are handled using a backstepping method. Compared with methods based on full state high-gain observer, this approach improves robustness with respect to measurement noise and avoids overparametrization. Semiglobal tracking is proven under the assumption that the regressor is persistently exciting View full abstract»

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  • Dynamic stabilization of regular linear systems

    Page(s): 4 - 21
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    We consider a general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in frequency domain. For this class of systems, we investigate the concepts of stabilizability and detectability, in particular, their invariance under feedback and their relationship to exponential stability. We introduce two concepts of dynamic stabilization, the first formulated as usual, with the plant and the controller connected in feedback, and the second with two feedback loops. Even for finite-dimensional systems, the second concept, stabilization with an internal loop in the controller, is more general. We argue that the more general concept is the natural one, and we derive sufficient conditions under which an observer-based stabilizing controller with an internal loop can be constructed View full abstract»

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  • Flexible piezoelectric structures-approximate motion equations and control algorithms

    Page(s): 94 - 101
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (272 KB)  

    Continuous-time and discrete-time algorithms are proposed to control a thin piezoelectric structure which can be described by means of approximate linear time-invariant dynamic models. Generalized coordinates are introduced to approximately represent the kinematics of the structure in a polynomial form; the approximate motion equations are determined by the application of the integral Hamilton principle in the Lagrangian form. The proposed control laws are designed on the basis of the obtained continuous-time and discrete-time approximate dynamic models; they guarantee the gravity force compensation, the noninteracting control of the generalized coordinates, and the asymptotic tracking of reference signals. Simulation results confirming the theoretical effectiveness of the algorithms are reported in the paper View full abstract»

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  • On the stability of uncertain systems with multiple time-varying delays

    Page(s): 101 - 105
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    In this paper, criteria for the global asymptotic stability of a class of uncertain systems with multiple time-varying delays are proposed. Based on the improved Razumikhin-type theorem, delay-dependent and delay-independent criteria are provided to guarantee the global asymptotic stability of such systems. Our main results are generalizations of some recent results reported in the literature in the case with multiple time-varying delays. A numerical example Is also given to illustrate our results View full abstract»

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  • Shear force feedback control of a single-link flexible robot with a revolute joint

    Page(s): 53 - 65
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    In this paper we present a shear force feedback control method for a single-link flexible robot arm with a revolute joint for which it has been shown that direct bending strain feedback can suppress its vibration. Our primary concern is the stability analysis of the closed-loop equation which has not appeared in the literature. We show the existence of a unique solution and the exponential stability of this solution by doing spectral analysis and estimating the norm of the resolvent operator associated with this equation. Some experiments are also conducted to verify these theoretical developments View full abstract»

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  • High-frequency nonlinear vibrational control

    Page(s): 83 - 90
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    This paper discusses the feasibility of high-frequency nonlinear vibrational control. Such control has the advantage that it does not require state measurement and processing capabilities that are required in conventional feedback control. Bellman et al. (1986) investigated nonlinear systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the Jacobian matrix has a positive trace. This paper extends previous work to include nonlinear vibrational controllers. A stability criteria is derived for nonlinear systems with nonlinear controllers, and it is shown that a nonlinear vibrational controller can stabilize a system even if the Jacobian matrix has a positive trace View full abstract»

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  • H-differential Riccati equations: convergence properties and finite escape phenomena

    Page(s): 113 - 118
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    The paper studies the transient and asymptotic behavior of the solution of the sign-indefinite differential Riccati equation (DRE) arising in finite-horizon H-filtering and control problems. Differently from the sign-definite H-DRE, the solution of the H-DRE can have finite escape times even for nonnegative initial conditions. Sufficient and necessary conditions for boundedness and convergence are derived in correspondence to a fixed value of the H-norm attenuation level γ. Finally, a stepwise γ-switching strategy is devised to guarantee boundedness as well as asymptotic performance View full abstract»

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  • Discrete-time low-gain control of uncertain infinite-dimensional systems

    Page(s): 22 - 37
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    Using a frequency-domain analysis, it is shown that the application of a feedback controller of the form k/(z-1) or kz/(z-1), where k∈R, to a power-stable infinite-dimensional discrete-time system with square transfer-function matrix G(z) will result in a power-stable closed-loop system which achieves asymptotic tracking of arbitrary constant reference signals, provided that i) all the eigenvalues of G(1) have positive real parts, and ii) the gain parameter k is positive and sufficiently small, Moreover, if G(1) is positive definite, we show how the gain parameter gain X can be tuned adaptively. The resulting adaptive tracking controllers are universal in the sense that they apply to any power-stable system with G(1)>0; in particular, they are not based on system identification or plant parameter estimation algorithms, nor is the injection of probing signals required. Finally, we apply these discrete-time results to obtain adaptive sampled-data low-gain controllers for the class of regular systems, a rather general class of infinite-dimensional continuous-time systems for which convenient representations are known to exist, both in state space and in frequency domain. We emphasize that our results guarantee not only asymptotic tracking at the sampling instants but also in the sampling interval View full abstract»

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  • On the relation between local controllability and stabilizability for a class of nonlinear systems

    Page(s): 90 - 94
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    The problem of local stabilizability of locally controllable nonlinear systems is considered. It is well known that, contrary to the linear case, local controllability does not necessarily imply stabilizability. A class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static-state feedback is described, as for this class of systems the well-known Hermes controllability condition is necessary and sufficient for local controllability View full abstract»

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  • New results for the bounds of the solution for the continuous Riccati and Lyapunov equations

    Page(s): 118 - 123
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    This paper presents upper and lower matrix bounds for the solution of the continuous algebraic matrix Riccati equation. Furthermore, a new lower matrix bound for the solution of the continuous algebraic Lyapunov equation is also developed. These are new results View full abstract»

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  • Persistent identification of time-varying systems

    Page(s): 66 - 82
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    Identification of time-varying systems, especially slowly time-varying systems, is of importance in the development of a comprehensive theory of adaptation. The persistent identification measures employed in this paper capture a main characterization in such identification problems, namely, one input signal must be used for identification of all possible observation windows. This paper establishes several essential features in persistent identification problems which highlight their potential utility in adaptation: 1) they have computable upper and lower bounds for typical classes of prior uncertainty sets; 2) any full rank n-periodic signals are optimal, and the simple least-squares estimates are optimal identification algorithms; 3) optimal probing inputs can be approximately generated in a closed-loop configuration when the plant and the controller are slowly time-varying; and 4) n-periodic signals are asymptotically optimal for slowly time-varying systems. The main results of this paper have been successfully combined with a certain slow H design to derive an adaptive stabilization scheme View full abstract»

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  • Indirect adaptive pole-placement control of MIMO stochastic systems: self-tuning results

    Page(s): 38 - 52
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    In this paper, we consider indirect adaptive pole-placement control (APPC) of linear multivariable stochastic systems. Instead of the canonical representation often used in the literature, we propose using a non-minimal but otherwise uniquely identifiable pseudo-canonical parameterization that is more suitable for multivariable ARMAX model identification. To identify the plant, we use the weighted extended least-squares (WELS) algorithm, a least-squares method with slowly decreasing weights which was introduced in Bercu (1995). The pole-placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable. We prove that with a reasonable amount of prior information, the resulting APPC scheme is globally stabilizing and asymptotically self-tuning regardless of the degree of persistency of external excitation. These results represent the most complete study of stochastic multivariable APPC systems to this date 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