State Observer Design for Nonlinear Systems Using Neural Network

Abstract

In this paper, an observer design is proposed for nonlinear systems. The Hamilton Jacobi Bellman (HJB) equation based formulation has been developed. The HJB equation is formulated using a suitable non­ quadratic term in the performance functional to tackle magnitude constraints on the observer gain. Utilizing Lyapunov s direct method, observer is proved to be optimal with respect to meaningful cost. In the present algorithm, neural network (NN) is used to approximate value function to nd approximate solution of HJB equation using least squares method. With time­varying HJB solution, we proposed a dynamic optimal observer for the nonlinear system. Proposed algorithm has been applied on nonlinear systems with nite­time­horizon and in nite­time­horizon. Necessary theoretical and simulation results are presented to validate proposed algorithm.