Design of Suboptimal Constrained Nonlinear Quadratic Regulator via Invariant Sets Switching

Abstract

A design method for a suboptimal constrained nonlinear quadratic regulator (CNLQR) via invariant sets switching is presented. The CNLQR has the merits of both the control invariant set and the gain scheduling, and solves the constrained nonlinear quadratic regulation problem effectively. It first calculates the equilibrium surface of the nonlinear system, and then obtains the off-line local LQR control laws and the corresponding control invariant sets for several equilibrium points. These control invariant sets cover the equilibrium surface such that the closed-loop stability of the nonlinear system can be guaranteed by switching the local LQR laws on-line. The algorithm is computationally efficient, because the state feedback control law and control invariant sets are all solved off-line so that the computational burden of on-line optimization is greatly reduced. A simulation example illustrating the method is presented.