Suboptimal Control of Constrained Nonlinear Systems via Receding Horizon State Dependent Riccati Equations (I)

Feedback stabilization of systems subject to constraints has been a long-standing problem in control theory. In contrast with the case of LTI plants where several techniques for optimizing performance have recently appeared, very few results are available for the case of nonlinear systems. In this paper we propose a new controller design method, based on the combination of Receding Horizon and Control Lyapunov Functions, for nonlinear systems subject to input constraints. The main result of the paper shows that this control law renders the origin an asymptotically stable equilibrium point in the entire region where stabilization with constrained controls is feasible, while, at the same time, achieving near-optimal performance.