A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability

摘要

We present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closedloop stability. The scheme can be applied to both stable and unstable systems with input constraints. The objective functional to beminimized consists of an integral square error (ISE) part over a finite time horizon plus a quadratic terminal cost. The terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate Lyapunov equation.Furthermore, the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region. If the Jacobian linearization of the nonlinear system to be controlled isstabilizable, we prove that feasibility of the open-loop optimal control problem at time t = 0 implies asymptotic stability of the closed-loop system. The size of the region of attraction is only restricted by the requirement for feasibility of theoptimization problem due to the input and terminal inequality constraints and is thus maximal in some sense.