In this paper, we study asymptotic properties of problems of control of stochastic discrete time systems with time averaging and time discounting optimality criteria, and we establish that the Cesàro and Abel limits of the optimal values in such problems can be estimated with the help of a certain infinite-dimensional (ID) linear programming (LP) problem and its dual.
The results of this paper are twofold. In the first part of the paper, we consider a discretetime stochastic control system and we show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the set of their mathematical expectations converge (as the time horizon tends to infinity) to a convex and compact (non-random) set, which is shown to coincide with the set of stationary probabilities of the system. In the second part, we apply the results obtained in the first part to deal with a hybrid system that evolves in continuous time and is subjected to abrupt changes of certain parameters. We show that the solutions of such a hybrid system are approximated by the solutions of a differential inclusion, the right-hand side of which is defined by the limit occupational measures set, the existence and convexity of which is established in the first part of the paper.
In this paper, we study asymptotic properties of problems of control of stochastic discrete time systems with time averaging and time discounting optimality criteria, and we establish that the Cesáro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinitedimensional (ID) linear programming (LP) problem and its dual.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.