Artículos de revistas
Uncoupled Riccati Iterations For The Linear Quadratic Control Problem Of Discrete-time Markov Jump Linear Systems
Registro en:
Ieee Transactions On Automatic Control. , v. 43, n. 12, p. 1727 - 1733, 1998.
189286
10.1109/9.736071
2-s2.0-0032290544
Autor
Do Val J.B.R.
Geromel J.C.
Costa O.L.V.
Institución
Resumen
This paper deals with recursive methods for solving coupled Riccati equations arising in the linear quadratic control for Markovian jump linear systems. Two algorithms, based on solving uncoupled Riccati equations at each iteration, are presented. The standard method for this problem relies on finite stage approximations with receding horizon, whereas the methods presented here are based on sequences of stopping times to define the terminal time of the approximating control problems. The methods can be ordered in terms of rate of convergence. Comparisons with other methods in the current literature are also presented. 43 12 1727 1733 Abou-Kandil, H., Freiling, G., Jank, G., On the solution of discrete-time Markovian jump linear quadratic control problems (1995) Automatica, 31 (5), pp. 765-768 Ait-Rami, M., Ghaoui, L.E., LMI optimization for nonstandard Riccati equations arising in stochastic control (1996) IEEE Trans. Automat. Contr., 41, pp. 1666-1671. , Nov Costa, O.L.V., Do Val, J.B.R., Geromel, J.C., A convex programming approach to H2-control of discrete-time Markovian jump linear systems (1997) Int. J. Contr., 66, pp. 557-579 Costa, O.L.V., Fragoso, M.D., Stability results for discrete-time linear systems with Markovian jumping parameters (1993) J. Math. Analysis and Appl., 179, pp. 154-178 Discrete-time LQ-optimal control problems for infinite Markov jump parameter systems (1995) IEEE Trans. Automat. Contr., 40, pp. 2076-2088 Davis, M.H.A., Vinter, R.B., (1985) Stochastic Modeling and Control, , London, U.K.: Chapman and Hall El Ghaoui, L., Nikoukhah, R., Delebecque, F., LMITOOL: A Front-End for LMI Optimization - User's Guide, , ftp.ensa.fr/pub/elghaoui/lmitool Fragoso, M.D., Ribeiro Do Val, J.B., Pinto Jr., D.L., Jump linear H∞-control: The discrete-time case (1995) Contr. Th. and Adv. Tech., 10, pp. 1459-1474 Gajic, Z., Borno, I., Lyapunov iterations for optimal control of jump linear systems at steady state (1995) IEEE Trans. Automat. Contr., 40 (11), pp. 1971-11075 Geromel, J.C., Peres, P.L.D., Souza, S.R., H2-guaranteed cost control for uncertain discrete-time linear systems (1993) Int. J. Contr., 57, pp. 853-864 Ji, Y., Chizeck, H.J., Controllability, observability and discrete-time Markovian jump linear quadratic control (1988) Int. J. Contr., 48, pp. 481-498 Ji, Y., Chizeck, H.J., Feng, X., Loparo, K.A., Stability and control of discrete-time jump linear systems (1991) Control Th. and Adv. Tech., 7, pp. 247-270 Laub, A., Algebraic aspects of generalized eigenvalue problems for solving Riccati equations (1986) Computational and Combinatorial Methods in Systems Theory, pp. 213-227. , C. Byrnes and A. Lindquist, Eds. Amsterdam, The Netherlands: Elsevier Mariton, M., (1990) Jump Linear Systems in Automatic Control, , New York: Marcel Dekker Vandenberghe, L., Boyd, S., Software for Semidefinite Programming - User's Guide, , isl.stanford.edu/pub/boyd/semidef_prog Wimmer, H.K., Monotonicity and maximality of solutions of discrete-time algebraic Riccati equations (1992) J. Math. Syst., Estimation and Contr., 2 (2), pp. 219-235