Application of terminal region enlargement approach for discrete time quasi infinite horizon nonlinear model predictive control

Abstract

SummaryEnsuring nominal asymptotic stability of the nonlinear model predictive control (NMPC) controller is not trivial. Stabilizing ingredients such as terminal penalty term and Terminal Region (TR) are crucial in establishing the asymptotic stability. Approaches available in the literature provide limited degrees of freedom for the characterization of the TR for the discrete time quasi infinite horizon NMPC formulation. Current work presents alternate approaches namely arbitrary controller based approach and linear quadratic regulator (LQR) based approach, which provide larger degrees of freedom for enlarging the TR. Both the approaches are scalable to system of any dimension. Approach from the literature provides a scalar whereas proposed approaches provide two additive matrices as tuning parameters for shaping of the TR. Proposed approaches involve solving modified Lyapunov equations to compute terminal penalty term, followed by explicit characterization of the TR. Efficacy of the proposed approaches is demonstrated using benchmark two state system. TR obtained using the arbitrary controller based approach and LQR based approach are approximately 10.4723 and 9.5055 times larger by area measure when compared to the largest TR obtained using the approach from the literature. As a result, there is significant reduction in the prediction horizon length while retaining the feasibility of the controller.