Nonlinear H/sub ∞/ controller design for a class of nonlinear control systems

Abstract

As a kind of robust control for nonlinear systems, nonlinear H/sub /spl infin// control has been developed in recent years. Since controller design requires the solution of a positive definite function from a nonlinear partial differential HJI inequality, and since no any efficient algorithms have been proposed for solving the inequality to date, a nonlinear H/sub /spl infin// controller is very difficult to realize in practice. In this paper, for a class of nonlinear control systems, a design method for nonlinear H/sub /spl infin// controllers is presented. By choosing a set of suitable penalty variables, the HJI inequality can be replaced by an algebraic matrix Riccati inequality. As an example, nonlinear H/sub /spl infin// tracking controllers for rigid robot arms are designed.