Robust Multi-step Model Predictive Control with Guaranteed Stability

Abstract

We present a method of ensuring recursive feasibility and input-to-state stability of 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 performs an a priori sufficient feasibility check of the robust nonlinear MPC optimisation problem, and uses information from previous solutions to provide a fallback based on previously certified prediction sets. We illustrate the proposed predictor-substitution strategy with a simple numerical example.