Hybrid evolutionary robust optimization-based optimal control for time-delay nonlinear systems

Optimal controls receive much attention owing to their remarkable performance for nonlinear systems. However, unknown time-delay disturbances in the optimal control process make it difficult to find high-quality optimal set points. To address this problem, a hybrid evolutionary robust optimization-based optimal control (HERO-OC) method is proposed to reduce the negative effect of time-delay disturbances and enhance the performance of optimal set points. First, a data-driven time-delay disturbance observer (DTDO), based on fuzzy neural networks, is designed to describe the time-delay disturbances of optimal objectives. Then, the expressions and intervals of time-delay disturbances can be estimated to improve the accuracy of optimal objectives. Second, a hybrid evolutionary robust optimization (HERO) algorithm, which combines an expectation robust optimization strategy with a min–max evolutionary robust optimization strategy, is proposed to solve optimal set points. Then, the average robustness and conservative of robustness optimal set points can be improved. Third, an adaptive time-delay controller using Lyapunov–Krasovskii functionals is proposed to track optimal set points. Then, control accuracy is improved while ensuring control stability. Finally, the superior performance of HERO-OC is compared with some novel optimal control methods in a second-order nonlinear system and a wastewater treatment process.