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

Optimal Control of Uncertain Nonlinear Quadratic Systems with Constrained Inputs