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

• Published in: Chaos, solitons and fractals Vol. 173; p. 113604
• Main Authors: Chen, Xin, Li, FuZhen, Yuan, Dongmei, Wang, Jian, Shao, Yu
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2023
• Subjects: Noncausal systems; Recurrence equations; Uncertain optimal control; Uncertainty theory; Recurrence equations; Noncausal systems; 49L20; 93C10; 93C05; Uncertain optimal control; 49N05; Uncertainty theory
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2023.113604

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. •Present uncertain random noncausal systems and convert them into subsystems.•Optimal control problems for uncertain random noncausal systems are transformed into equivalent problems.•Recurrence equations are presented to transform these problems into solving problems for deterministic difference equations.•Analytical solutions of five kinds of optimal control problems are obtained.•Corresponding difference equations for solving time-delayed optimal control problem are given.