Optimal control problems subject to uncertain random discrete-time noncausal systems

Uncertain random discrete-time noncausal systems (URDTNSs) and optimal control problems (OCPs) are investigated under the framework of chance theory with chance expectation in this paper. We convert OCPs subject to URDTNSs into conditional equivalent uncertain random OCPs employing an algebraic transformation method. Then recurrence equations are proposed accordingly to transform the uncertain random OCPs into solving problems for deterministic difference equations. The OCPs having linear and quadratic objective functions along with three kinds of URDTNSs involving linear, quadratic, and cubic control terms are studied. As a generalization of the main findings, we study two types of OCPs for time-delayed URDTNSs and give a unified framework for solving such problems. Meanwhile, analytical expressions of optimal solutions for these kinds of OCPs are acquired. Furthermore, numerical examples are offered to highlight the usefulness of our results.