Design and analysis of constrained nonlinear quadratic regulator

Abstract

A suboptimal dual-mode solution to constrained nonlinear quadratic regulator (CNLQR) problem is studied. In a neighborhood of the origin, the controller is formulated as an LQR based on a model obtained by linearizing the original model at the origin. Outside this neighborhood, the control law is obtained by solving a finite horizon optimization problem (FHOP) with additional terminal inequality constraints. The terminal inequality constraints make the terminal states of FHOP be driven into the neighborhood of the origin, which is a specially designed control invariant set with respect to LQR control law. The overall control law is obtained by combining that obtained by solving FHOP and that obtained form LQR. The feasibility aspect is analyzed and asymptotic stability is proven. The effectiveness of this suboptimal controller is demonstrated by simulation studies.