On the discrete time-varying JLQG problem

Adam Czornik; Andrzej Świerniak

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 2, page 203-207
  • ISSN: 1641-876X

Abstract

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In the present paper optimal time-invariant state feedback controllers are designed for a class of discrete time-varying control systems with Markov jumping parameter and quadratic performance index. We assume that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Moreover, following the same line of reasoning, an adaptive controller is proposed in the case when system parameters are unknown but their strongly consistent estimators are available.

How to cite

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Czornik, Adam, and Świerniak, Andrzej. "On the discrete time-varying JLQG problem." International Journal of Applied Mathematics and Computer Science 12.2 (2002): 203-207. <http://eudml.org/doc/207580>.

@article{Czornik2002,
abstract = {In the present paper optimal time-invariant state feedback controllers are designed for a class of discrete time-varying control systems with Markov jumping parameter and quadratic performance index. We assume that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Moreover, following the same line of reasoning, an adaptive controller is proposed in the case when system parameters are unknown but their strongly consistent estimators are available.},
author = {Czornik, Adam, Świerniak, Andrzej},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {time-varying systems; coupled Riccati equations; jump linear systems; optimal control; adaptive control},
language = {eng},
number = {2},
pages = {203-207},
title = {On the discrete time-varying JLQG problem},
url = {http://eudml.org/doc/207580},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Czornik, Adam
AU - Świerniak, Andrzej
TI - On the discrete time-varying JLQG problem
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 2
SP - 203
EP - 207
AB - In the present paper optimal time-invariant state feedback controllers are designed for a class of discrete time-varying control systems with Markov jumping parameter and quadratic performance index. We assume that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Moreover, following the same line of reasoning, an adaptive controller is proposed in the case when system parameters are unknown but their strongly consistent estimators are available.
LA - eng
KW - time-varying systems; coupled Riccati equations; jump linear systems; optimal control; adaptive control
UR - http://eudml.org/doc/207580
ER -

References

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  1. Abou-Kandil H., Freiling G. and Jank G. (1994): Solution and asymptotic behavior of coupled Riccati equations in jump linear systems. -IEEE Trans. Automat. Contr., Vol. 39, No. 8, pp. 1631-1636. Zbl0925.93387
  2. 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
  3. Caines P.E. and Zhang J.F. (1995): On adaptive control of jump parameter systems via nonlinear filtrating. - SIAM J. Contr.Optim., Vol. 33, No. 6, pp. 1758-1777. Zbl0843.93076
  4. Costa O.L.V. and Fragoso M.D. (1995): Discrete-time LQ-optimal control problems for infinite Markov jump parameter systems. - IEEE Trans. Automat. Contr., Vol. 40, No. 12, pp. 2076-2088. Zbl0843.93091
  5. Chizeck H.J., Willsky A.S. and Castanon D. (1986): Discrete-time Markovian-jump linear quadratic optimal control. - Int. J. Contr., Vol. 43, No. 1, pp. 213-231. Zbl0591.93067
  6. Czornik A. (1998): On time-varying LQG. - Prep. IFACConf. System Structure and Control, France, Nantes, pp. 427-432. 
  7. Czornik A. (1999): On discrete-time linear quadratic-control. -Syst. Contr. Lett., Vol. 36, No. 2, pp. 101-107. Zbl0914.93068
  8. Czornik A. (2000): Continuity of the solution of the Riccati equations for continuous time JLQP. - IEEE Trans. Automat. Contr., Vol. 45, No. 5, pp. 934-937. Zbl0977.34062
  9. Czornik A. (2002): Adaptive control for jump linear system with quadratic cost. - Int. J. Adapt. Contr. Signal Process., (submitted). Zbl1121.49034
  10. Czornik A. and Świerniak A. (2001): On the discrete JLQ and JLQG problems. - Nonlin. Anal., Vol. 47, No. 1, pp. 423-434. Zbl1042.49537
  11. Dufour F. and Bertrand P. (1994): Stabilizing control law for hybrid models. - IEEE Trans. Automat. Contr., Vol. 38, No. 11, pp. 2354-2357. Zbl0825.93698
  12. Dufor F. and Elliott R. (1998): Adaptive control for linear systems with markov perturbations. - IEEE Trans. Automat. Contr., Vol. 43, No. 3, pp. 351-372. 
  13. Ghosh M.K. (1995): A note on an LQG regulator with Markovian switching and pathwise average cost. - IEEE Trans. Automat. Contr., Vol. 40, No. 2, pp. 1919-1921. Zbl0843.93090
  14. Ghaoui L. (1996): LMI optimization for nonstandard Riccati equations arising in stochastic control. - IEEE Trans. Automat. Contr., Vol. 41, No. 11, pp. 1666-1671. Zbl0863.93087
  15. Griffiths B.E. and Loparo K. (1985): Optimal control of jump-linear gaussian systems. - Int. J. Contr., Vol. 42, No. 4, pp. 791-819. Zbl0583.93070
  16. 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
  17. Ji Y. and Chizeck H.J. (1989): Optimal quadratic control of jump linear systems with separately controlled transition probabilities. -Int. J. Contr., Vol. 49, No. 2, pp. 481-491. Zbl0677.93071
  18. Mariton M. (1987): Jump linear quadratic control with random state discontinuities. - Automatica, Vol. 23, No. 2, pp. 237-240. Zbl0628.93074
  19. Pan G. and Bar-Shalom Y. (1996): Stabilization of jump linear gaussian systems without mode observations. - Int. J. Contr., Vol. 64, No. 4, pp. 631-666. Zbl0857.93095
  20. Sworder D.D. (1969): Feedback control of a class of linear systems with jump parameters. - IEEE Trans. Automat. Contr., Vol. 14, No. 1, pp. 9-14. 
  21. Sworder D.D. and Robinson V.G. (1973): Feedback regulators for jump parameter systems with state and control dependent transition rates. -IEEE Trans. Automat. Contr., Vol. 18, No. 4, pp. 355-359. Zbl0279.93059

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