Coevolution-Based Robust Optimal Control for Nonlinear System With Time-Delay Optimal Objectives

Abstract

Due to its demonstrated efficacy, optimal control has extensive application in nonlinear systems. However, in the optimal control process, the time delays in the optimization objectives makes the optimization problem difficult to solve. To improve the optimal control performance, a coevolution-based robust optimal control (C-TDROC) method is designed. First, a data-driven estimation strategy is proposed to approximate the optimal objectives of nonlinear systems. Then, the approximation errors caused by time delays are described as uncertain representations of system states. Second, a coevolution-based robust optimization (CRO) algorithm is developed to solve the optimal set points of system states. This algorithm generates two coevolutionary particle swarms in robust time delay intervals to improve the robustness of optimal set points. Third, an adaptive time delay controller is proposed for tracking the optimal set points. Then, the Lyapunov-Krasovskii functionals are employed to ensure the stability of C-TDROC. The experiments on a time-delay nonlinear system and a time-delay biochemical reaction process are carried out to prove the availability of C-TDROC.