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Solutions for the Linear-Quadratic Control Problem of Markov Jump Linear Systems

Author

Listed:
  • J. B. R. Do Val

    (University of Campinas)

  • J. C. Geromel

    (University of Campinas)

  • O. L. V. Costa

    (University of São Paulo)

Abstract

The paper is concerned with recursive methods for obtaining the stabilizing solution of coupled algebraic Riccati equations arising in the linear-quadratic control of Markovian jump linear systems by solving at each iteration uncoupled algebraic Riccati equations. It is shown that the new updates carried out at each iteration represent approximations of the original control problem by control problems with receding horizon, for which some sequences of stopping times define the terminal time. Under this approach, unlike previous results, no initialization conditions are required to guarantee the convergence of the algorithms. The methods can be ordered in terms of number of iterations to reach convergence, and comparisons with existing methods in the current literature are also presented. Also, we extend and generalize current results in the literature for the existence of the mean-square stabilizing solution of coupled algebraic Riccati equations.

Suggested Citation

  • J. B. R. Do Val & J. C. Geromel & O. L. V. Costa, 1999. "Solutions for the Linear-Quadratic Control Problem of Markov Jump Linear Systems," Journal of Optimization Theory and Applications, Springer, vol. 103(2), pages 283-311, November.
    • Handle: RePEc:spr:joptap:v:103:y:1999:i:2:d:10.1023_a:1021748618305
    DOI: 10.1023/A:1021748618305
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    Cited by:

    1. J.B.R. Do Val & E.F. Costa, 2002. "Numerical Solution for Linear-Quadratic Control Problems of Markov Jump Linear Systems and Weak Detectability Concept," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 69-96, July.
    2. O. L. V. Costa & J. C. C. Aya, 2001. "Temporal Difference Methods for the Maximal Solution of Discrete-Time Coupled Algebraic Riccati Equations," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 289-309, May.

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