Control of Nonlinear Systems with Uncertainty

Abstract

In this chapter, we consider nonlinear systems with time-varying uncertain variables and present robust inverse optimal controller designs that enforce an arbitrary degree of attenuation of the effect of uncertainty on the output of the closed-loop system. The controller designs are obtained by re-shaping the scalar nonlinear gain of Sontag's formula in a way that guarantees the desired uncertainty attenuation properties in the closed-loop system. The proposed re-shaping is made different for vanishing and non-vanishing uncertainties so as to meet different robustness and optimality objectives.