An Approximate Realization of Nonlinear H_∞ Control Based on Hamilton-Jacobi Equation

Abstract

In this paper, a novel numerical approach of the Hamilton-Jacobi Equation (HJE) in the nonlinear H_∞ control problems is proposed. First of all, it is assumed that the solution of the HJE is an extended quadratic form, and a state-dependent Riccati Equation (sRE) is derived. Next, the solution of the sRE is approximated with a polynominal matrix by the least square method, and the approximated solution of the HJE is selected as the extended quadratic form approximately corresponding to this polynominal. Our proposal is applied to an inverted pendulum system, and its validity is shown through simulations as compared with the linear H_∞ control and the nonlinearH_∞ control based on the conventional methods.