Robust H^∞ control of a nonlinear uncertain system via a stable nonlinear output feedback controller

A new approach to solving a nonlinear robust H^∞ control problem using a stable nonlinear output feedback controller is presented in this article. The class of nonlinear uncertain systems being considered is characterised in terms of integral quadratic constraints and global Lipschitz conditions describing the admissible uncertainties and nonlinearities, respectively. The nonlinear controller is able to exploit the plant nonlinearities through the inclusion of a copy of the known plant nonlinearities in the controller. The H^∞ control objective is to obtain an absolutely stable closed-loop system with a specified disturbance attenuation level. The solution to this control problem involves stabilising solutions to parametrised algebraic Riccati equations. We apply a differential evolution algorithm to solve a non-convex nonlinear optimisation problem arising in the controller synthesis.