Optimal multilevel control of stochastic dynamical system with state delay and indefinite cost matrices

Abstract

In this paper, optimal control of stochastic dynamical system with delay in the state and multilevel control and indefinite cost matrices is studied. Conditions of optimality using the maximum principle are considered. A finite planning horizon linear quadratic problem of the system and its reduction to an algebraic Riccati equation are studied. The resultant Riccati equation is formulated as a semidefinite programming problem. The distinctive features of the problem under consideration are that the stochastic system has delay in the state with a multilevel control and cost matrices are allowed to be indefinite.