General LQ problem for infinite jump linear systems and the minimal solution of algebraic Riccati equations

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 16, Issue , 2005, Pages 1-6

  Costa, Eduardo F ^a   Do Val, João Bosco R ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Algebraic Riccati equations; Linear quadratic regulators; Linear systems; Markov parameters

Indexed keywords

ALGEBRA; FEEDBACK CONTROL; LINEAR SYSTEMS; MARKOV PROCESSES;

ALGEBRAIC RICCATI EQUATIONS; COUPLED ALGEBRAIC RICCATI EQUATIONS; DETERMINISTIC SYSTEMS; GENERAL OPTIMIZATIONS; LINEAR QUADRATIC REGULATOR; LQ CONTROL PROBLEM; MARKOV JUMP PARAMETER; MARKOV PARAMETERS;

RICCATI EQUATIONS;

EID: 79960715114     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20050703-6-cz-1902.00352     Document Type: Conference Paper

References (19)

1. Athans, M., D. Castanon, K. P. Dunn, C. S. Greene, W. H. Lee, N. R. Sandell and A. S. Willsky (1977). The stochastic control of the F- 8C aircraft using a multiple model adaptive control (MMAC) method - Part i: Equilibrium flight. IEEE Transactions on Automatic Control 22, 768-780.
2. Costa, E. F. and J. B. R. do Val (2002a). On the detectability and observability of continuous-time Markov jump linear systems. SIAM Journal on Control and Optimization 41(4), 1295-1314.
3. Costa, E. F. and J. B. R. do Val (2002b). Weak detectability and the linear quadratic control problem of discrete-time Markov jump linear systems. International Journal of Control. Special issue on Switched and Polytopic Linear Systems 75, 1282-1292.
4. Costa, E. F. and J. B. R. do Val (n.d.). An algorithm for solving a perturbed algebraic Riccati equation. To appear in the European Journal of Control.
5. Costa, E. F., J. B. R. do Val and M. D. Fragoso (n.d.a). A new approach to detectability of discrete-time infinite Markov jump linear systems. To appear in the SIAM Journal on Control and Optimization.
6. Costa, E. F., J. B. R. do Val and M. D. Fragoso (n.d. b). On a detectability concept of discrete-time infinite Markov jump linear systems. To appear in the Stochastic Analysis and Applications.
7. Costa, O. L. V. and M. D. Fragoso (1995). Discrete-time LQ-optimal control problems for infinite Markov jump parameter systems. IEEE Transactions on Automatic Control AC-40, 2076-2088.
8. 2-control for discrete-time Markovian jump linear systems. International Journal of Control 73(1), 11-21.
9. 2 control of discrete-time Markovian jump linear systems. Int. J. Control 66(4), 557-579.
10. 2-control of Markovian jump linear systems via convex analysis. Automatica 35, 259-268.
11. do Val, J. B. R. and E. F. Costa (2002). Numerical solution for the linear-quadratic control problem of Markov jump linear systems and a weak detectability concept. Journal of Optimization Theory and Applications 114(1), 69-96.
12. do Val, J. B. R., J. C. Geromel and O. L. V. Costa (1999). Solutions for the linear quadratic control problem of Markov jump linear systems. Journal of Optimization Theory and Applications 103, 283-311.
13. Fragoso, M. and J. Baczynski (2001). Optimal control for continuous time LQ problems with infinite Markov jump parameters. SIAM Journal on Control and Optimization 40(1), 270-297.
14. Ji, Y. and H. J. Chizeck (1990). Controlability, stabilizability and continuous time Markovian jump linear quadratic control. IEEE Transactions on Automatic Control 35(7), 777-788.
15. Kucera, V. (1972). On nonnegative definite solutions to matrix quadratic equations. Automatica 8, 413-423.
16. Martensson, K. (1971). On the matrix Riccati equation. Inform. Sci. 3, 17-49.
17. Molinari, B. P. (1977). The time-invariant linear-quadratic optimal control problem. Automatica 13, 347-357.
18. Rami, M. A. and L. E. Ghaoui (1996). LMI optimization for nonstandard Riccati equations arising in stochastic control. IEEE Transactions on Automatic Control 41(11), 1666-1671.
19. Sworder, D. D. and R. O. Rogers (1983). An LQ-solution to a control problem associated with a solar thermal central receiver. IEEE Transactions on Automatic Control 28(10), 971-978.