Continuation Method for Nonsmooth Model Predictive Control Using Proximal Technique

A study conducted by Ryotaro Shima et al. was selected for presentation at The 2025 American Control Conference (ACC).

Model predictive control (MPC) determines control inputs through optimization while predicting the future behavior of a system, and it is widely used in industrial applications such as automotive control. One practical implementation of MPC is the continuation method, which accelerates the computation of control inputs by exploiting a system of linear equations.

Recently, optimization problems incorporating non-differentiable regularization terms have attracted increasing attention. However, it has remained unclear how the continuation method can be applied to MPC formulations involving such non-differentiable regularizers.

In this study, we propose a novel theoretical framework for applying the continuation method to MPC with non-differentiable regularization terms. The proposed approach enables the combination of flexible MPC design and fast optimization, and is expected to facilitate the realization of more advanced control systems.

Title: Continuation Method for Nonsmooth Model Predictive Control Using Proximal Technique
Authors: Shima, R., Moriyasu, R., Kato, T.
Appears in: The 2025 American Control Conference （ACC）
Presented: July 10, 2025