Optimal Control of Uncertain Nonlinear Quadratic Systems with Constrained Inputs

Abstract

This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances, and in presence of some amplitude constraints on the control input. By using an approach based on the guaranteed cost control theory, a technique is proposed to design a state feedback controller ensuring for the closed-loop system: i) the local exponential stability of the zero equilibrium point; ii) the inclusion of a given region into the domain of exponential stability of the equilibrium point; iii) the satisfaction of a guaranteed level of performance, in terms of boundedness of some optimality indexes. In particular, a sufficient condition for the existence of a state feedback controller satisfying a prescribed integral-quadratic index is provided, followed by a sufficient condition for the existence of a state feedback controller satisfying a given $\mathcal L_2$-gain disturbance rejection constraint. By the proposed design procedures, the optimal control problems dealt with here can be efficiently solved as Linear Matrix Inequality (LMI) optimization problems.