A Model Predictive Control Algorithm

ABSTRACT: We apply a Model Predictive Control (MPC) algorithm to a finite-horizon continuous-time optimal control problem with nonlinear dynamics, an integral cost, control constraints and a parameter which represents uncertainty. We consider the question under what conditions the MPC-generated control is a good approximation of an optimal feedback control of the continuous-time system. We give an answer to that question based on the concept of uniform strong regularity. Specifically, under a coercivity condition and a condition that the optimal control is an isolated solution of the variational inequality in the maximum principle, we establish uniform Lipschitz stability of the discretized problem, the existence of an optimal feedback control, uniform convergence of the Newton/SQP method, as well as an estimate for the difference between the MPC-generated control and the optimal feedback control.