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Automatic Control, IEEE Transactions on

Issue 8 • Date Aug. 1989

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Displaying Results 1 - 25 of 26
  • Comments, on "A generalization of Rosenbrock's theorem" by M. Schlegel

    Page(s): 921 - 922
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (189 KB)  

    In the above paper (ibid., vol.AC-32, p.155, Feb. 1987) the author presents a generalization of the famous Rosenbrock theorem concerning the problem of synthesis of linear state feedback control laws for linear controllable systems. The commenters point out that this result was published by them earlier (in an alternative form). Here they give again alternative conditions for solvability of the problem, since the original papers (published in 1979 and 1985) were in Russian. In contrast to the conditions given in the above paper, their conditions are not redundant and are given in terms of order relation on the lattice of integer partitions.<> View full abstract»

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  • Comments on functional reproducibility of time-varying input-output systems

    Page(s): 922 - 924
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    Recent results on solvability developed as part of a conjecture of K.A. Grasse (SIAM J. Contr. Optimiz., vol.26, p.230-249, 1988) on the necessity of certain rank conditions is answered for an important class of systems. A simpler description of the derivative arrays is presented. An alternative way of computing the control producing a given output is presented.<> View full abstract»

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  • Indirect adaptive control for interconnected systems

    Page(s): 908 - 911
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    An indirect adaptive controller for interconnected systems is introduced. Each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems. A variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances. An adaptive state feedback control law is described which stabilizes the interconnected system, forcing the input and output signals of each subsystem to remain bounded View full abstract»

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  • Exact recursive polyhedral description of the feasible parameter set for bounded-error models

    Page(s): 911 - 915
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (444 KB)  

    A method is described which exactly characterizes the set of all the values of the parameter vector of a linear model that are consistent with bounded errors on the measurements. It provides a parameterized expression of this set, which can be used for robust control design or for optimizing any criterion over the set. This approach is based on a new variant of the double description method for determining the edges of a polyhedral cone. It can be used in real time and provides a suitable context for implementation on a computer. Whenever a new measurement modifies the set, the characterization is updated. The technique is illustrated with a simple example View full abstract»

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  • Compensating for computational delay in digital equivalent of continuous control systems

    Page(s): 895 - 899
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (376 KB)  

    A computer-aided method to compensate for the computational delay in the digital equivalent of continuous control systems is presented. The objective is to obtain the transfer function of the digital controller so that the performance of the equivalent digital control system is as close to that of the existing continuous system as possible. This is done by matching the frequency response of the digital control system to that of the existing system with a minimum weighted mean-square error. A formula for computing the parameters of the digital controller is obtained as a result. The design method is illustrated with an example View full abstract»

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  • An SDR algorithm for the solution of the generalized algebraic Riccati equation

    Page(s): 875 - 879
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    An algorithm is presented for solving certain classes of the algebraic Riccati equation by using the MDR transformation and extending the symplectic QR-like (or SR) method of A. Bunse-Gerstner (Linear Alg. Applic., vol.83, p.49-78, 1986) and V. Mehrmann (Ph.D. Diss., Univ. Bielefeld, W. Germany) to the generalized eigenvalue problem. The Riccati equations arise from linear systems of the form Edx/dt=Ax+Bu, where E is nonsingular but for numerical reasons E-1 A and E-1 B cannot be computed reliably View full abstract»

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  • Robust stabilization of normalized coprime factor plant descriptions with H-bounded uncertainty

    Page(s): 821 - 830
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    The problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by H bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system. This problem can be reduced to a Nehari extension problem directly and gives an optimal stability margin. All controllers satisfying a suboptimal stability margin are characterized, and explicit state-space formulas are given View full abstract»

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  • Necessary and sufficient conditions for robust stabilization of an observer-based compensating system suffering nonlinear time-varying perturbation

    Page(s): 899 - 900
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    It is demonstrated that the robust stabilization against additive nonlinear time-varying uncertainty presented by B.S. Chen and W.S. You (ibid., vol.AC-32, p.1131-5, Dec. 1987) is not just a sufficient but also a necessary condition. An additional necessary and sufficient condition that arises in the case of multiplicative uncertainty is also discussed View full abstract»

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  • Flow balance equations for the steady-state distribution of a flexible manufacturing system

    Page(s): 917 - 921
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    Flow balance equations are formulated for the steady-state distribution of machine state and production surplus when a flexible manufacturing system is operated under a feedback control law. The long-run average cost is equal to the expectation in steady state of the instantaneous expenditure rate if the system is ergodic, and the optimum in a given family of control laws can be obtained by minimizing this cost criterion. Although the equations have a very intuitive interpretation, analytic solutions are known only in the one-dimensional case when a single commodity is produced according to a hedging point strategy View full abstract»

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  • Dissipative LQG control systems

    Page(s): 866 - 870
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    An indefinite Lyapunov test matrix for closed-loop dissipativeness using LQG (linear quadratic Gaussian) design is presented. The application of this test to relaxation systems, lossless systems, Hamiltonian systems, positive real systems, and second-order systems with collocated rate sensors and actuators is explored. The Lyapunov test also helps clarify the role of collocated sensors and actuators in LQG design. A set of duality theorems based on the indefinite Lyapunov test matrix is derived View full abstract»

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  • Minimal realization of transfer function matrices via one orthogonal transformation

    Page(s): 893 - 895
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    The minimal realization of a given arbitrary transfer function matrix G(s) is obtained by applying one orthogonal similarity transformation to the controllable realization of G( s). The similarity transformation is derived by computing the QR or the singular value decomposition of a matrix constructed from the coefficients of G(s). It is emphasized that the procedure has not been proved to be numerically stable. Moreover, the matrix to be decomposed is larger than the matrices factorized during the step-by-step procedures given View full abstract»

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  • A simple algorithm on minimal balanced realization for transfer function matrices

    Page(s): 879 - 882
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB)  

    Given a transfer function matrix, it is shown that its minimal balanced realization can be obtained directly from the singular values and the singular vectors of a constant matrix constructed from the coefficients of the least common denominator polynomial. The algorithm is based on the close relationship of controllability and the observability gramians to the singular value decomposition of the associated infinite block Hankel matrix View full abstract»

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  • On the robustness of sampled-data control to unmodeled high-frequency dynamics

    Page(s): 900 - 903
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB)  

    Robustness of sampled-data control designs to unmodeled high-frequency dynamics is studied using singular perturbation theory. It is argued that when the plant is preceded by a zero-order hold, a direct transmission term of the reduced-order model, which results from neglecting high-frequency dynamics, should be modeled as a delay element in order to ensure robustness View full abstract»

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  • On L1 optimal control

    Page(s): 884 - 885
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    It is shown that the problem of minimizing the effect of the worst disturbance on the output, where the signals have finite one norms, is equivalent to the same problem with bounded disturbances. The following situations provide the motivation to study such a problem. (1) Disturbances are generated by a fixed bounded-input, bounded-output (BIBO) stable, linear time-invariant (LTI) system with unknown initial conditions and zero input. (The output of this fixed system is the disturbance input to the original control system). (2) Disturbances are generated by an unknown BIBO stable LTI system whose fixed input consists of the unit impulse (this is the dual of (1)). In both of these situations, the disturbances will have a finite one norm View full abstract»

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  • An approach for pole assignment in singular systems

    Page(s): 889 - 893
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    Pole assignment in a singular system Edx/dt=Ax+Bu is discussed. It is shown that the problem of assigning the roots of det(sE-(A +BF)) by applying a proportional feedback u=Fx+r in a given singular system is equivalent to the problem of pole assignment of an appropriate regular system. An immediate application of this result is that procedures and computational algorithms that were originally developed for assigning eigenvalues in regular systems become useful tools for pole assignment in singular systems. The approach provides a useful tool for the combined problem of eliminating impulsive behavior and stabilizing a singular system View full abstract»

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  • Graph topology and gap topology for unstable systems

    Page(s): 848 - 855
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    A reformation is provided of the graph topology and the gap topology for a general setting (including lumped linear time-invariant systems and distributed linear time-invariant systems) in the frequency domain. Some essential properties and their comparisons are clearly presented in the reformulation. It is shown that the gap topology is suitable for general systems rather than square systems with unity feedback. It is shown that whenever an unstable plant can be stabilized by feedback, it is a closed operator, mapping a subspace of the input space to the output space. Hence, the gap topology can always be applied whenever the unstable plant can be stabilized. The graph topology and the gap topology are suitable for different subsets of systems and have many similar characteristics. If one confines them to the same subset, they will be identical. The definitions of the graph metric and the gap metric are discussed View full abstract»

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  • A globally convergent algorithm with adaptively refined discretization for semi-infinite optimization problems arising in engineering design

    Page(s): 903 - 908
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (496 KB)  

    Although most of the algorithms that have been proposed for the solution of semi-infinite optimization problems make use, at each iteration, of a set of local maximizers over the range of the independent parameter, the question of suitably approximating such maximizers is generally left aside. It has been suggested that this issue can be addressed by means of an adaptively refined discretization of the interval of variation of the independent parameter. The algorithm proposed in the paper makes use of such a technique and, by means of a certain memory mechanism, avoids the potential lack of convergence suffered by an existing algorithm, while requiring a relatively small number of gradient evaluations View full abstract»

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  • A real Schur form method for modeling singularly perturbed systems

    Page(s): 856 - 861
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    A method is presented for modeling a two-time-scale system in the singularly perturbed form. The method uses an ordered real Schur decomposition, which can be efficiently computed using standard subroutines from EISPACK. Three results are given. First, it is shown that any two-time-scale system can be modeled in the singularly perturbed form by a transformation into an ordered real Schur form, followed by balancing. Second, under some conditions on the ordered real Schur decomposition, a procedure is given to achieve the modeling task with all fast variables chosen from the original state variables. Third, necessary and sufficient conditions are given to achieve modeling by permutation of the original state variables View full abstract»

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  • Robust stability for time-delay systems: the edge theorem and graphical tests

    Page(s): 813 - 820
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    The robust stability problem is discussed for a class of uncertain delay systems where the characteristic equations involve a polytope P of quasi-polynomials (i.e. polynomials in one complex variable and exponential powers of the variable). Given a set D in the complex plane, the goal is to find a constructive technique to verify whether all roots of every quasi-polynomial in P belong to D (that is, to verify the D-stability of P). First it is demonstrated by counterexample that Kharitonov's theorem does not hold for general delay systems. Next it is shown that under a mild assumption on the set D a polytope of quasi-polynomials is D-stable if and only if the edges of the polytope are D-stable. This extends the edge theorem for the D-stability of a polytope of polynomials. The third result gives a constructive graphical test for checking the D-stability of a polytope of quasi-polynomials which is especially simple when the set D is the open left-half plane. An application is given to demonstrate the power of the results View full abstract»

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  • Data reduction in the mixed-sensitivity H design problem

    Page(s): 861 - 865
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    The mixed-sensitivity H design problem is discussed in the two-block case. The state-space approach is used to investigate the internal structure of this design problem, which inherits many pole-zero cancellations. The complete state-space solution is provided. Efficient mathematical software can then be implemented View full abstract»

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  • Sensitivity considerations in the control of generalized plants

    Page(s): 885 - 888
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    A comparison sensitivity matrix is derived for a generalized plant for which the controlled and measured variables are not necessarily the same. The sensitivity of the control signal to plant and controller parameter variations is characterized. It is shown that sensitivity reduction is possible only when the controlled and measured variables are appropriately related. A relationship between comparison sensitivity and exogenous signal attenuation is shown View full abstract»

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  • A comparison of two linear methods of estimating the parameters of ARMA models

    Page(s): 915 - 917
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    A finite-order stationary and minimum-phase ARMA (autoregressive moving-average) (p,q) model is equivalent to an infinite-order AR (autoregressive) model. Two methods of estimating the parameters of the ARMA (p,q) model by solving only linear equations are based on or closely related to this equivalence relation. One method was derived directly from the equivalence relation by D. Graupe et al. (ibid., vol.AC-20, p.104-107, Feb. 1975). The other was derived by S. Li and B.W. Dickinson (ibid., vol.AC-31, p.275-278, Mar. 1986 and IEEE Trans. Acoust. Speech Signal Process., vol.ASSP-36, p.502-512, Apr. 1988) based on an iterated least-squares regression approach. The end results bear close resemblance to those of Graupe et al. The two methods are compared, and ways to improve the parameter estimates are suggested View full abstract»

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  • Robust stabilization of linear time-invariant systems

    Page(s): 870 - 875
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    The problem of robustly stabilizing families of linear time-variant plants consisting of a nominal plant and its frequency domain neighborhood is discussed. Necessary and sufficient conditions are obtained for robust stabilizability of such families of plants. The set of robustly stabilizing controllers is parameterized and the largest achievable stability margin is characterized for a linear time-invariant plant View full abstract»

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  • Controller reduction: concepts and approaches

    Page(s): 802 - 812
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    The problem of passing from a linear time-invariant high-order controller designed for a linear time-invariant plant (of presumably high order) to a low-order approximation of the controller is discussed. The approximation problem is often best posed as a frequency-weighted L approximation problem. Many different controller representations are possible, giving different performances of the various reduction algorithms View full abstract»

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  • On computing the infinity norm

    Page(s): 882 - 884
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    An iterative algorithm is given for computing the infinity norm of the transfer matrix of a bounded, linear, time-invariant, finite-dimensional system. The procedure, which is based on the numerically stable QZ algorithm, enables the infinite norm to be computed with a guaranteed accuracy. No ad hoc procedures, such as those for selecting a suitable grid of frequencies, for example, are used. The degree of accuracy is under the direct control of the user, with each additional decimal place of accuracy requiring ≈3.3 calls to the QZ algorithm. Experience has shown the algorithm to function reliably and in reasonable time for models of order as large as 56 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