Robust inverse optimal control laws for nonlinear systems

Abstract

AbstractThis work proposes a robust inverse optimal controller design for a class of nonlinear systems with bounded, time‐varying uncertain variables. The basic idea is that of re‐shaping the scalar nonlinear gain of an LgV controller, based on Sontag's formula, so as to guarantee certain uncertainty attenuation properties in the closed‐loop system. The proposed gain re‐shaping is shown to yield a control law that enforces global boundedness of the closed‐loop trajectories, robust asymptotic output tracking with an arbitrary degree of attenuation of the effect of uncertainty on the output, and inverse optimality with respect to a meaningful cost that penalizes the tracking error and the control action. The performance of the control law is illustrated through a simulation example and compared with other controller designs. Copyright © 2003 John Wiley & Sons, Ltd.