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2002 | 12 | 4 | 539-543
Tytuł artykułu

Continuity of solutions of Riccati equations for the discrete-time JLQP

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The continuity of the solutions of difference and algebraic coupled Riccati equations for the discrete-time Markovian jump linear quadratic control problem as a function of coefficients is verified. The line of reasoning goes through the use of the minimum property formulated analogously to the one for coupled continuous Riccati equations presented by Wonham and a set of comparison theorems.
Rocznik
Tom
12
Numer
4
Strony
539-543
Opis fizyczny
Daty
wydano
2002
otrzymano
2001-06-05
poprawiono
2002-04-24
Twórcy
autor
  • Department of Automatic Control, Silesian University of Technology, ul. Akademicka 16, 44-101 Gliwice, Poland
  • Department of Automatic Control, Silesian University of Technology, ul. Akademicka 16, 44-101 Gliwice, Poland
Bibliografia
  • Abou-Kandil H., Freiling G. and Jank G. (1995): On the solution of discrete-time Markovian jump linear quadratic control problems. - Automatica, Vol. 31, No. 5, pp. 765-768.
  • Bourles H., Jonnic Y. and Mercier O. (1990): ρ-Stability and robustness: Discrete time case. - Int. J. Contr., Vol. 52, No. 2, pp. 1217-1239, .
  • Chen H.F. (1985): Recursive Estimation and Control for Stochastic Systems. - New York: Wiley.
  • Chizeck H.J., Willsky A.S. and Castanon D. (1986): Discrete-time Markovian linear quadratic optimal control. - Int. J. Contr., Vol. 43, No. 1, pp. 213-231.
  • Chojnowska-Michalik A., Duncan T.E. and Pasik-Duncan B. (1992): Uniform operator continuity of the stationary Riccati equation in Hilbert space. - Appl. Math. Optim., Vol. 25, No. 2, pp. 171-187.
  • Czornik A. (1996): Adaptive control in linear system with quadratic cost functional. - Matematyka Stosowana (Applied Mathematics), Vol. 39, No. 1, pp. 17-39, (in Polish).
  • Czornik A. (2000): Continuity of the solution of the Riccati equations for continuous time JLQP. - IEEE Trans. Automat. Contr., Vol. 45, pp. 934-937.
  • Czornik A. and Sragovich W. (1995): On asymptotic properties of algebraic Riccati equations for continuous time. - Automat. Remote Contr., Vol. 56, No. 8, pp. 1126-1128.
  • Delchamps D.F. (1980): A note on the analityicity of the Riccati metric, In: Lectures in Applied Mathematics (C.I. Byrnes and C.F. Martin, Eds.). - Providence, RI: AMS, pp. 37-41.
  • Faibusovich L.E. (1986): Algebraic Riccati equation and sympletic algebra. - Int. J. Contr., Vol. 43, No. 3, pp. 781-792.
  • Ji Y. and Chizeck H.J. (1988): Controllability, observability and discrete-time Markovian jump linear quadratic control. - Int. J.Contr., Vol. 48, No. 2, pp. 481-498.
  • Lancaster P. and Rodman L. (1995): Algebraic Riccati Equation. - Oxford: Oxford Univ. Press.
  • Rodman L. (1980): On extremal solution of the algebraic Riccati equation, In: Lectures in Applied Mathematics (C.I. Byrnes and C.F. Martin, Eds.). - Providence, RI: AMS, pp. 311-327.
  • Wonham W.M. (1971): Random differential equations in control theory, In: Probabilistic Methods in Applied Mathematics (A.T. Bharucha-Reid, Ed.). - New York: Academic Press, Vol. 2.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-amcv12i4p539bwm
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