Method of Adaptive Control of Pure Feedback Plants Based on the Actor-Critic Framework

Abstract

This article proposes a backstepping-based method for design of adaptive control for uncertain pure feedback nonlinear systems using reinforcement learning. Pure feedback nonlinear systems describe classes of electromechanical systems, mobile robots, and moving objects. When setting the problem, the constraints on control and state variables of the plant were taken into account. The adaptive control problem is solved using the one-step Actor-Critic method. Radial basis functions are used to approximate the control policy. To estimate the value of a state, an analytical expression is used that depends on the control error at two time steps. A new algorithm for updating weight coefficients and parameters of radial basis functions is proposed. The article demonstrates the effect of increasing the accuracy of a closed-loop system by dynamically adjusting the parameters of radial basis functions. The proposed algorithm does not contain uncertainty in calculating the increments of weight coefficients. The closed-loop Lyapunov stability property of the system is demonstrated. The theoretical analysis is supported by numerical simulation examples.