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

Adam Czornik; Andrzej Świerniak

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 4, page 539-543
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Czornik, Adam, and Świerniak, Andrzej. "Continuity of solutions of Riccati equations for the discrete-time JLQP." International Journal of Applied Mathematics and Computer Science 12.4 (2002): 539-543. <http://eudml.org/doc/207609>.

@article{Czornik2002,
abstract = {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.},
author = {Czornik, Adam, Świerniak, Andrzej},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {jump parameter system; stochastic stabilizability; observability; coupled algebraic Ricatti equations; robustness; quadratic control; sensitivity; coupled algebraic Riccati equations; quadratic control problem},
language = {eng},
number = {4},
pages = {539-543},
title = {Continuity of solutions of Riccati equations for the discrete-time JLQP},
url = {http://eudml.org/doc/207609},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Czornik, Adam
AU - Świerniak, Andrzej
TI - Continuity of solutions of Riccati equations for the discrete-time JLQP
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 4
SP - 539
EP - 543
AB - 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.
LA - eng
KW - jump parameter system; stochastic stabilizability; observability; coupled algebraic Ricatti equations; robustness; quadratic control; sensitivity; coupled algebraic Riccati equations; quadratic control problem
UR - http://eudml.org/doc/207609
ER -

References

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  1. 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. Zbl0822.93074
  2. 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, . Zbl0707.93057
  3. Chen H.F. (1985): Recursive Estimation and Control for Stochastic Systems. - New York: Wiley. 
  4. 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. Zbl0591.93067
  5. 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. Zbl0762.93044
  6. 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). Zbl0871.93030
  7. Czornik A. (2000): Continuity of the solution of the Riccati equations for continuous time JLQP. - IEEE Trans. Automat. Contr., Vol. 45, pp. 934-937. Zbl0977.34062
  8. 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. Zbl0925.34058
  9. 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. 
  10. Faibusovich L.E. (1986): Algebraic Riccati equation and sympletic algebra. - Int. J. Contr., Vol. 43, No. 3, pp. 781-792. Zbl0559.93020
  11. 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. Zbl0669.93007
  12. Lancaster P. and Rodman L. (1995): Algebraic Riccati Equation. - Oxford: Oxford Univ. Press. Zbl0836.15005
  13. 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. 
  14. 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. Zbl0223.93045

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