Robust Multi-step Model Predictive Control with Feasibility Guarantees

Abstract

We present a method of ensuring recursive feasibility and stability for robust nonlinear Model Predictive Control (MPC) with multi-step predictors. Although feasibility guarantees are well-established for the case of single-step models applied recursively over a finite horizon, such guarantees are missing in naive MPC formulations that use distinct multi-step models to predict the system state at different future points in time. This issue arises because of potential inconsistencies in multi-step predictions generated at different times. Our approach checks for possible infeasibility of the robust nonlinear MPC optimisation problem \textit{a priori}, and uses information from previous solutions to provide a fall-back based on previously verified reachable sets. We illustrate the proposed predictor-substitution strategy with a simple numerical example.