Robust Multi-step Model Predictive Control with Guaranteed Stability

Sebastian Steffen; Mark Cannon

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arXiv · 2606.25684

Robust Multi-step Model Predictive Control with Guaranteed Stability

Sebastian Steffen·Mark Cannon

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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.

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Sebastian Steffen, Mark Cannon. 2026-06-24. Robust Multi-step Model Predictive Control with Guaranteed Stability. https://arxiv.org/abs/2606.25684

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