A Survey of Learning in Optimal Control and Differential Game

With the widespread applications of large-scale multi-agent systems, optimal control and differential game have become essential components of modern control theory. However, traditional methods often struggle with the inherent challenges posed by high dimensionality when addressing high-dimensional problems. The rapid development of deep learning has provided new solution ideas and methods to address this challenge. This paper reviews the research status and progress of solution methods for optimal control and differential game. First, this review elaborates on the fundamental theoretical frameworks of optimal control theory for continuous-time systems and differential game. Second, this paper introduces in detail two main deep learning methods: Deep Reinforcement Learning (DRL) and Physics-Informed Deep Learning (PIDL). Based on this, this study analyzes the specific applications of these two methods in addressing the aforementioned problems. Finally, this article summarizes the main problems and limitations of existing research and points out future research directions.