A Prediction-Correction Method for Model Predictive Control

In this work we adapt a prediction-correction algorithm for continuous time-varying convex optimization problems to solve dynamic programs arising from Model Predictive Control (MPC). The algorithm proposed is computationally efficient since it finds an approximate solution of the problem with only two Hessian inversions per iteration. The error in the approximation as compared to solving the MPC problem exactly is of the order of the square of the sampling time. This computationally efficient solution allows to extend the applicability of Model Predictive Control to systems with faster dynamics and less computational power. Numerical examples where we consider a highly nonlinear system support the theoretical conclusions.