Optimal Control for a Multistage Uncertain Random System

Chance theory is a mathematical methodology for modelling complex systems including both uncertainty and randomness. Based on chance theory, this paper introduces the optimal control model for a multistage uncertain random system. For solving such a model, recurrence equations are presented via Bellman’s principle. With the aid of recurrence equations, the bang-bang problem of optimal control model and indefinite linear quadratic (LQ) problem of optimal control model are studied. Meanwhile, the exact solutions of such problems are presented. Furthermore, numerical examples are provided on the proposed theorems to show the effectiveness of our results.