Reinforcement Learning Based Adaptive Predefined-Time Optimal Control for Strict-Feedback Nonlinear Systems

An adaptive predefined-time optimal control method based on fuzzy logic system (FLS) is presented in this paper for strict-feedback nonlinear systems. The settling time of predefined-time control can be set in advance, which is independent of the design parameters and initial conditions. The optimal control relies on solving the Hamilton-Jacobi-Bellman (HJB) equation, which is difficult to calculate directly due to its inherent nonlinearity. To overcome this difficulty, the reinforcement learning (RL) strategy of actor-critic structure is used, where the actor and critic are used to achieve control behavior and evaluate system performance, respectively. In addition, the RL algorithm is simplified, and the two conditions of persistence of excitation and known dynamics required for the most optimal controls are eliminated. The main objective of this article is to ensure that the tracking error converges to a small neighborhood near the origin within a predefined time, while minimizing energy consumption. Finally, the efficiency of the suggested control strategy is demonstrated by using a practical simulation example.