Prescribed-Time Adaptive Fuzzy Optimal Control for Nonlinear Systems

The prescribed-time optimal control problem for nonlinear systems is investigated in this paper. First, a transformation function is constructed, which includes the system state and a strictly decreasing auxiliary function related to the prescribed time and accuracy. Second, the control input and the transformation function are incorporated into a new performance index function (PIF). This encodes the prescribed-time control into the optimal control problem. Subsequently, a new Hamilton-Jacobi-Bellman (HJB) equation related to the prescribed time and accuracy is derived. To find a solution to the HJB equation, a fuzzy reinforcement learning algorithm is proposed. This algorithm successfully approximates the optimal cost and control policy while ensuring the system stability. Additionally, the system state can converge to a pre-assigned residual set within a prescribed time. Finally, an example of an electromechanical system is used to illustrate the efficacy of the suggested algorithm.