Optimal control for uncertain random singular systems with multiple time-delays.

• Present an optimal control model with multiple time-delays in uncertain random environments. • A method is presented to transform the problem into an equivalent optimization problem. • Propose the recurrence equations to solve the optimization problem. • The optimal solutions of two kinds of optimization problems are obtained. Chance theory provides us a useful tool to solve an optimal control problem with indeterminacy composing of both uncertainty and randomness. Based on chance theory, this paper studies an optimal control for uncertain random singular systems with multiple time-delays. First, an uncertain random singular system with multiple time-delays is introduced, and then the corresponding optimal control problem is established. The equivalent relationship between this problem and the optimal control problem for standard uncertain random systems is derived. Then the appropriate recurrence equations are proposed according to the dynamic programming method. Furthermore, two kinds of optimal control problems are discussed. The optimal control inputs and respective optimal values of the problems are provided via the solvability of the obtained equations. Finally, a numerical example is presented to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]