Dual-mode Nonlinear MPC via Terminal Control Laws With Free-parameters

The paper presents a new dual-mode nonlinear model predictive control (NMPC) scheme for continuous-time nonlinear systems subject to constraints on the state and control. The idea of control Lyapunov functions for nonlinear systems is used to compute the terminal regions and terminal control laws with some free-parameters in the dual-mode NMPC framework. The parameters of the terminal controller are selected offline to estimate the terminal region as large as possible; and the parameters are optimized online to gain optimality of the terminal controller with respect to given cost functions. Then a dual-mode NMPC algorithm with varying time-horizon is formulated for the constrained system. Recursive feasibility and closed-loop stability of this NMPC are established. The example of a spring-cart is used to demonstrate the advantages of the presented scheme by comparing to the dual-mode NMPC via the linear quadratic regulator (LQR) method.