Actas de congresos
Finite Approximation Of The Optimal Average Cost For A Class Of Stochastic Control Systems
Registro en:
9783902661937
Ifac Proceedings Volumes (ifac-papersonline). , v. 18, n. PART 1, p. 12427 - 12431, 2011.
14746670
10.3182/20110828-6-IT-1002.03711
2-s2.0-84866759997
Autor
Vargas A.N.
Do Val J.B.R.
Institución
Resumen
This paper provides conditions for which the optimal finite-stage cost, divided by the number of stages, converges to the optimal long-run average cost as the number of stages goes to infinity. The main condition is based on a controllability to the origin property. The discrete-time stochastic system is linear with respect to the system state but the control possess a general structure, possibly nonlinear. To illustrate the effectiveness of the result, an application to the simultaneous state-feedback control problem is considered. © 2011 IFAC. 18 PART 1 12427 12431 Anderson, B.D.O., Moore, J.B., (1979) Optimal Filtering, , Prentice-Hall, Englewood Cliffs, N.J Arapostathis, A., Borkar, V.S., Fernández-Gaucherand, E., Ghosh, M.K., Marcus, S.I., Discrete-time controlled Markov processes with average cost criterion: A survey (1993) SIAM J. Control Optim., 31 (2), pp. 282-344 Bertsekas, D.P., Shreve, S.E., (1978) Stochastic Optimal Control: The Discrete Time Case, , Academic Press Cho, Y.-Y., Lam, J., A computational method for simultaneous LQ optimal control design via piecewise constant output feedback (2001) IEEE Trans. Systems Man Cybernetics Part B, 31, pp. 836-842 Do Val, J.B.R., Başar, T., Receding horizon control of jump linear systems and a macroeconomic policy problem (1999) J. Econom. Dynam. Control, 23, pp. 1099-1131 Geromel, J.C., Peres, P.L.D., Souza, S.R., H 2- guaranteed cost control for uncertain discrete-time linear systems. Int (1993) Journal of Control, 57, pp. 853-864 Hernández-Lerma, O., Lasserre, J.B., (1996) Discrete-Time Markov Control Processes: Basic Optimality Criteria, , Springer-Verlag, New York Howitt, G.D., Luus, R., Control of a collection of linear systems by linear state feedback control (1993) Int. Journal Control, 58 (1), pp. 79-96 Lavaei, J., Aghdam, A.G., Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions (2007) Automatica, 43 (2), pp. 274-280 Luke, R.A., Dorato, P., Abdallah, C.T., Linear-quadratic simultaneous performance design (1997) Proc. American Control Conf., pp. 3602-3605 Meyn, S.P., The policy iteration algorithm for average reward Markov decision processes with general state space (1997) IEEE Trans. Automat. Control, 42 (12), pp. 1663-1680 Saadatjooa, F., Derhami, V., Karbassi, S.M., Simultaneous control of linear systems by state feedback (2009) Computers Math. Appl., 58 (1), pp. 154-160 Schal, M., Average optimality in dynamic programming with general state space (1993) Math. Oper. Res., 18, pp. 163-172 Sennott, L.I., The convergence of value iteration in average cost Markov decision chains (1996) Oper. Res. Lett., 19, pp. 11-16 Vargas, A.N., Do Val, J.B.R., Minimum second moment state for the existence of average optimal stationary policies in linear stochastic systems (2010) Proc. American Control Conference, pp. 373-377. , Baltimore, MD, USA Vargas, A.N., Do Val, J.B.R., Average optimal stationary policies: Convexity and convergence conditions in linear stochastic control systems (2009) Proc. 48th IEEE Conf. Decision Control and 28th Chinese Control Conference, pp. 3388-3393. , Shangai, China Vargas, A.N., Do Val, J.B.R., A controllability condition for the existence of average optimal stationary policies of linear stochastic systems (2009) Proc. European Control Conference, pp. 32-37. , Budapest, Hungary Vargas, A.N., Do Val, J.B.R., Costa, E.F., Receding horizon control of Markov jump linear systems subject to noise and unobservable state chain (2004) Proc. 43th IEEE Conf. Decision Control, pp. 4381-4386 Wu, J.-L., Lee, T.-T., Optimal static output feedback simultaneous regional pole placement (2005) IEEE Trans. Systems Man Cybernetics Part B, 35, pp. 881-893