Nonlinear Model Predictive Control with Parameter-Dependent Terminal Penalty

We propose a quasi-infinite horizon nonlinear model predictive control with terminal inequality constraint and terminal state quadratic penalty. The feasibility of terminal state inequality constraint implies the states at the end of the horizon are in a prescribed asymptotically stable but not necessarily invariant ellipsoidal set in terms of an auxiliary parameter-dependent quadratic Lyapunov function. The terminal state penalty matrix of the terminal penalty item is to be chosen as parameter-dependent matrix. The technology relaxes terminal state inequality constraint and reduces the state penalty in terminal stable set. Then two stabilizing nonlinear model predictive control algorithms are proposed based on a sequence of asymptotically stable parameter-dependent ellipsoidal set computed offline with different upper bound