# On adaptive control for the continuous time-varying JLQG problem

Adam Czornik; Andrzej Świernik

International Journal of Applied Mathematics and Computer Science (2005)

- Volume: 15, Issue: 1, page 53-62
- ISSN: 1641-876X

## Access Full Article

top## Abstract

top## How to cite

topCzornik, Adam, and Świernik, Andrzej. "On adaptive control for the continuous time-varying JLQG problem." International Journal of Applied Mathematics and Computer Science 15.1 (2005): 53-62. <http://eudml.org/doc/207727>.

@article{Czornik2005,

abstract = {In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can be estimated through strongly consistent estimators.},

author = {Czornik, Adam, Świernik, Andrzej},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {time varying systems; adaptive control; JLQG problem},

language = {eng},

number = {1},

pages = {53-62},

title = {On adaptive control for the continuous time-varying JLQG problem},

url = {http://eudml.org/doc/207727},

volume = {15},

year = {2005},

}

TY - JOUR

AU - Czornik, Adam

AU - Świernik, Andrzej

TI - On adaptive control for the continuous time-varying JLQG problem

JO - International Journal of Applied Mathematics and Computer Science

PY - 2005

VL - 15

IS - 1

SP - 53

EP - 62

AB - In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can be estimated through strongly consistent estimators.

LA - eng

KW - time varying systems; adaptive control; JLQG problem

UR - http://eudml.org/doc/207727

ER -

## References

top- 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
- 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
- Afanas'ev V.N., Kolmanovskij V.B. and Nosov V.R. (1989): Mathematical Theory of Control System Design. - Moscow: Vyssha Shkola, (in Russian).
- Blom H.A.P.(1990): Bayesian estimation for decision-directed stochastic control. - Amsterdam, The Netherlands: Technical Univ. Delft Press.
- Boukas E.K. and Haurie A. (1990): Manufacturing flow control andpreventive maintenance: A stochastic control approach - IEEE Trans. Automat. Contr., Vol. 35, No. 9, pp. 1024-1031. Zbl0718.90036
- Costa 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, pp. 2076-2088. Zbl0843.93091
- Chizeck H.J., Willsky A.S. and Castanon D. (1998): Discrete-time markovian-jump linear quadratic optimal control. -Int. J. Contr., Vol. 43, No. 2, pp. 213-231. Zbl0591.93067
- Czornik A. (1998): On time-varying LQG. - Proc. IFAC Conf. Syst. Struc. Contr., Nantes, France, pp. 427-432.
- Czornik A. (1999): On discrete-time linear quadratic-control. - Syst. Contr. Lett., Vol. 36, No. 2, pp. 101-107. Zbl0914.93068
- 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
- Czornik A. and Swierniak A. (2001): On the discrete JLQ and JLQG problems. - Nonlin. Anal., Vol. 47, No. 1, pp. 423-434. Zbl1042.49537
- Czornik A. and Swierniak A. (2002): On the discrete time-varying JLQG problem. - Int. J. Appl. Math. Comput. Sci., Vol. 12, No. 2, pp. 101-105. Zbl1049.93087
- Czornik A. (2004): Adaptive control for jump linear system with quadratic cost. - Contr. Cybern., Vol. 33, No. 1, pp. 51-71 . Zbl1121.49034
- Czornik A. and Swierniak A. (2004): On the continuous time-varying JLQ problem. - Europ. J. Contr, Vol. 10, No. 3, pp. 264-272. Zbl1293.49077
- Duncan T.E., Guo L. and Pasik-Duncan B. (1999): Adaptive continous-time linear quadratic gaussian control. - IEEE Trans. Automat. Contr., Vol. 44, No. 9, pp. 1653-1662. Zbl0963.93080
- Dufour F. and Elliott R. (1998): Adaptive control for linear systems with Markov perturbations. - IEEE Trans. Automat.Contr., Vol. 43, No. 3, pp. 351-372. Zbl0919.93085
- Feng X., Loparo K.A., Ji Y. and Chizeck H.J. (1992): Stochastic stability properties of jump linear systems. - IEEE Trans. Automat. Contr., Vol. 37, No. 3, pp. 38-53. Zbl0747.93079
- Ghosh M.K. (1995): On an LQG regulator with Markovian switching and pathwise average cost. - IEEE Trans. Automat. Contr., Vol. 40, No. 4, pp. 1919-1921. Zbl0843.93090
- Griffiths B.E. and Loparo K. (1985): Optimal control of jump-linear Gaussian systems. - Int. J. Contr., Vol. 42, No. 5, pp.791-819. Zbl0583.93070
- Guo L. (1996): Self-convergence of weighted least-squares with applications to stochastic adaptive control. - IEEE Trans. Automat. Contr., Vol. 41, No. 1, pp. 79-89. Zbl0844.93081
- Ji Y. and Chizeck H.J. (1988): Controllability, observability and discrete-time Markovian jump linear quadratic control. - Int. J. Contr., Vol. 48, No. 6, pp. 481-498. Zbl0669.93007
- Ji Y. and Chizeck H.J. (1989): Optimal quadratic control of jump linear systems with seperately controlled transition probabilities. - Int. J. Contr., Vol. 49, No. 2, pp. 481-491. Zbl0677.93071
- Ji Y. and Chizeck H.J. (1990): Controllability, stability, and continuous-time Markovian jump linear quadratic control. - IEEE Trans. Automat. Contr., Vol. 35, No. 7, pp. 777-788. Zbl0714.93060
- Mariton M. (1987): Jump linear quadratic control with random state discontinuities. - Automatica, Vol. 23, No. 3, pp. 237-140. Zbl0628.93074
- Mariton M. (1990): Jump Linear Systems in Automatic Control.- New York: Marcel Dekker.
- Pan G. and Bar-Shalom Y. (1996): Stabilization of jump linear Gaussian systems without mode observations. - Int.J. Contr., Vol. 64, No. 7, pp. 631-666. Zbl0857.93095
- Prandini M. and Campi M.C. (2001): Adaptive LQG control of input-output systems: A cost-biased approach. - SIAM J. Contr.Optim., Vol. 39, No. 5, pp. 1499-1519. Zbl0989.93098
- Rami Ait M. and El Ghaoui L. (1996): LMI optimization for nonstandard Riccati equations arising in stochastic control. - IEEE Trans. Automat. Contr., Vol. 41, No. 10, pp. 1666-1671. Zbl0863.93087
- Siljak D.D. (1980): Reliable control Using Multiple Control Systems. - Int. J. Contr., Vol. 31, No. 2, pp. 303-329. Zbl0428.93033
- Świerniak A., Simek K. and Boukas E.K. (1998): Intelligent robust control of fault tolerant systems, In: Artificial Intelligence in Real-Time Control (H.E. Rauch, Ed.). - Oxford: Elsevier, pp. 245-248.
- Sworder D.D. and Rogers R.O. (1983): An LQ-solution to a control problem associated with solar thermal central receiver. - IEEE Trans. Automat. Contr., Vol. 28, No. 4, pp. 971-978.
- Sworder D.D. (1969): Feedback control of a class of linear systems with jump parameters. - IEEE Trans. Automat. Contr., Vol. 14, No. 4, pp. 9-14.
- 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. 3, pp. 355-359. Zbl0279.93059
- Wonham W.M. (1971): Random differential equations in control theory, In: Probabilistic Methods in Applied Mathematics, Vol. 2 (A.T. Bharucha-Reid, Ed.). - New York: Academic Press. Zbl0223.93045

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.