LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEM WITH A RANDOM HORIZON

Abstract

In this paper a Linear-Quadratic control model of a discrete-time is considered (the transition law is a linear difference equation and the cost per stage has a quadratic form). Also, the expected total cost with a random horizon is considered as performance criterion, it is assumed that the horizon is independent of the control process. For the corresponding control problem the existence of the optimal solution is proved when the support of the distribution of the horizon is infinite, the proof is based on recent theoretical results concerning to the Markov decision processes with a random horizon. In addition, the rolling horizon procedure is used to obtain a control policy
for the approximation of the optimal solution in the Linear-Quadratic control problem. The policy is provided through recursive equations which are programmed. In numerical cases is observed that even the policies with a small length of the rolling horizon provide good performance and a convergence of selectors in the policy of rolling horizon is observed, which allow to change the policy of rolling horizon by a stationary policy.