Reinforcement Learning‐Based Optimal Prescribed‐Time Tracking Control for Strict‐Feedback Systems With Unknown Affine Terms
TL;DR
A novel prescribed‐time optimal (PTO) tracking control scheme for nonlinear strict‐feedback systems with unknown affine terms based on radial basis function (RBF) neural networks is proposed and it is demonstrated for the first time that the critic‐actor weights can converge exponentially to the same values.
Abstract
This article proposes a novel prescribed‐time optimal (PTO) tracking control scheme for nonlinear strict‐feedback systems with unknown affine terms based on radial basis function (RBF) neural networks. First, by combining the barrier Lyapunov function method, a simple coordinate transformation is used to enable the system's tracking performance to be artificially set. Subsequently, at each step of the backstepping method, reinforcement learning algorithms with critic‐actor structures are introduced to design the optimal virtual controllers and the actual controller by finding solutions to Hamilton–Jacobi–Bellman (HJB) equations for the corresponding subsystems. Meantime, the complexity of system stability analysis caused by PT optimal control is overcome by appropriately decomposing ideal virtual controllers and the ideal actual controller. Based on the new HJB equation with PT characteristics, the easy‐to‐implement critic‐actor updating laws are designed by introducing tracking error as a driving term. It is demonstrated for the first time that, under the persistent excitation (PE) condition, the critic‐actor weights can converge exponentially to the same values. Finally, simulation and experimental results illustrate the effectiveness of the proposed control scheme.