Nonlinear model predictive control with semi-contracting constraint and generalized terminal constraint

In this paper, a new model predictive control (MPC) with semi-contracting constraint and generalized terminal constraint is proposed for a class of discrete time nonlinear systems. The generalized terminal constraint is based on the cost function, and the corresponding updating law is constructed by using the terminal cost in the previous sampling time. A semi-contracting constraint is employed to guarantee the asymptotic convergence of the closed-loop system without sacrificing feasibility of optimization. With assumptions on initial feasibility and reachability of the optimal fixed point, recursive feasibility and asymptotic convergence are proved theoretically. The theoretical results are illustrated by a simulation example.