An Overview of Optimal Control Methods for Singularly Perturbed Systems

Optimal control design methods for multiple time-scale systems are a hot research topic in recent years. In this paper, a comprehensive overview of the design methods for optimal control of multiple time-scale systems is presented. Firstly, the mathematical model of the optimal control problem of multiple time-scale systems is given, and the key difficulties of the related research are analysed. Secondly, the design methods for optimal control of multiple time-scale systems based on the model and reinforcement learning (RL) methods are given respectively. Thirdly, the performance analysis and practical application of the multi-time scale system are analyzed. Finally, the current problems in solving the optimization of multiple time-scale systems are analysed, and the research directions of optimal control of multiple time-scale systems are prospected.