Solutions for the linear-quadratic control problem of Markov jump linear systems

Journal of Optimization Theory and Applications

Volumn 103, Issue 2, 1999, Pages 283-311

  Do Val, J B R ^a   Geromel, J C ^a   Costa, O L V ^b  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Linear quadratic control; Markov jump linear systems; Nonstandard Riccati equation; Stopping time problems

Indexed keywords

ALGEBRA; ITERATIVE METHODS; LINEAR CONTROL SYSTEMS; MARKOV PROCESSES;

'CURRENT; COUPLED ALGEBRAIC RICCATI EQUATIONS; LINEAR QUADRATIC CONTROL PROBLEM; LINEAR-QUADRATIC CONTROLS; MARKOV JUMP LINEAR SYSTEMS; NONSTANDARD RICCATI EQUATION; RECURSIVE METHODS; STABILIZING SOLUTIONS; STOPPING TIME PROBLEMS;

RICCATI EQUATIONS;

EID: 0033269095     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021748618305     Document Type: Article

References (16)

1. ABOU-KANDIL, H., FREILING, G., and JANK, G., Solution and Asymptotic Behavior of Coupled Riccati Equations in Jump Linear Systems, IEEE Transactions on Automatic Control, Vol. 39, pp. 1631-1636, 1994.
2. AIT-RAMI, M., and EL GHAOUI, L., LMI Optimization for Nonstandard Riccati Equations Arising in Stochastic Control, IEEE Transactions on Automatic Control, Vol. 41, pp. 1666-1671, 1996.
3. BORNO, I., Parallel Computation of the Solutions of Coupled Algebraic Lyapunov Equations, Automatica, Vol. 31, pp. 1345-1347, 1995.
4. 2-Control of Discrete-Time Markovian Jump Linear Systems, International Journal of Control, Vol. 66, pp. 557-579, 1997.
5. DO VAL, J. B. R., GEROMEL, J. C., and COSTA, O. L. V., Uncoupled Riccati Iterations for the Linear-Quadratic Control Problem of Discrete-Time Markov Jump Linear Systems, IEEE Transactions on Automatic Control, Vol. 43, pp. 1727-1733, 1998.
6. FENG, X., LOPARO, K. A., JI, Y., and CHIZECK, H. J., Stochastic Stability Properties of Jump Linear Systems, IEEE Transactions on Automatic Control, Vol. 37, pp. 38-53, 1992.
7. GAJIC, Z., and BORNO, I., Lyapunov Iterations for Optimal Control of Jump Linear Systems at Steady State, IEEE Transactions on Automatic Control, Vol. 40, pp. 1971-1975, 1995.
8. GAJIC, Z., and LOSADA, R., Monotonicity of Algebraic Lyapunov Iterations for Optimal Control of Jump Parameter Linear Systems, Preprint, Rutgers University, 1997.
9. JI, Y., and CHIZECK, H. J., Controllability, Observability, and Continuous-Time Markovian Jump Linear-Quadratic Control, IEEE Transactions on Automatic Control, Vol. 35, pp. 777-788, 1990.
10. MARITON, M., Jump Linear Systems in Automatic Control, Marcel Dekker, New York, New York, 1990.
11. FRAGOSO, M. D., COSTA, O. L. V., and DE SOUZA, C. E., A New Approach to Linarly Perturbed Riccati Equations Arising in Stochastic Control, Applied Mathematics and Optimization, Vol. 37, pp. 99-126, 1998.
12. DAVIS, M. H. A., Markov Models and Optimization, Chapman and Hall, London, England, 1993.
13. KLEINMAN, D. L., On an Iterative Technique for Riccati Equation Computations, IEEE Transactions on Automatic Control, Vol. 13, pp. 114-115, 1968.
14. WONHAM, W., On a Matrix Riccati Equation of Stochastic Control, SIAM Journal on Control and Optimization, Vol. 6, pp. 681-697, 1968.
15. WONHAM, W., Random Difference Equations in Control Theory, Probabilistic Methods in Applied Mathematics, Edited by A. Bharucha-Reid, Academic Press, New York, New York, pp. 131-212, 1971.
16. OLIVEIRA, M. C., FARIA, D. P., and GEROMEL, J. C., LMIsol User's Guide, Available at http://dt.fee.unicamp.br/~carvalho/#soft.