Nonlinear Control System with Reinforcement Learning and Neural Networks Based Lyapunov Functions

Abstract

This paper deals with the problem of finding thecontrol Lyapunov function (CLF) that keeps the system stable. Two feedforward artificial neural networks are proposed as a function approximator to generate a control Lyapunov function for a nonlinear dynamical system without any local approximation of their dynamics. Finding a CLF is not an easy task. Then, to determine the control Lyapunov function, this paper proposes the use of reinforcement learning with two artificial neural networks based on the Lyapunov stability theory. The proposed control is applied in two nonlinear dynamical systems. To analyze the stability of the systems, the region of attraction (ROA) of an asymptotically stable equilibrium point was used. The simulations show the good performance of the proposed technique and confirmed that reinforcement learning and neural networks are an excellent mathematical tool to deal with control design problems and may lead to better solutions to nonlinear problems in the design of stable controls without linear approximations.