ADP-Based Prescribed-Time Control for Nonlinear Time-Varying Delay Systems With Uncertain Parameters

In this paper, we investigate the problem of prescribed-time optimal control using reinforcement learning technology. Unlike finite/fixed-time control methods that only achieve stability within specified time bounds, we propose a prescribed-time adaptive dynamic programming (ADP) control approach that ensures both optimality and prescribed-time stability. To address the challenge of solving the nonlinear Hamilton-Jacobi-Bellman (HJB) equation in finite horizon, we construct an actor-critic neural network (NN) with a time-varying activation function. The novel weight update laws are derived from the system's terminal error and the approximate error of the HJB equation. This derivation eliminates the need for knowledge of dynamic conditions while ensuring compliance with terminal constraints. Based on the proposed prescribed time stability criterion, the control scheme is proven to satisfy prescribed time stability while also ensuring optimal system performance index and bounded weights. We apply the designed control scheme in a time-varying delay system and simulation examples validate the efficacy of the strategy. Note to Practitioners - Many industrial processes are nonlinear time-varying delay systems, which brings great challenges to solving the HJB equation of the prescribed-time control problem. Therefore, it is of great value to solve the prescribed-time control problem by using the advantages of finite time ADP in solving the time-varying HJB equation. The ADP-based prescribed-time optimal control (ADPPTC) scheme designed in this paper aims to optimize the steady-state performance of nonlinear time-varying delay systems, and because the user can prescribe the stability time, the system can accurately complete a task within a specific time range. At the same time, the prior demand for the system state can be eliminated by the proposed actor-critic neural network.