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arXiv · 2603.21070

Koopman-Based Linear MPC for Safe Control using Control Barrier Functions

Shuo Liu·Liang Wu·Dawei Zhang·Jan Drgona·Calin. A. Belta
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Abstract

This paper proposes a Koopman-based linear model predictive control (LMPC) framework for safety-critical control of nonlinear discrete-time systems. Existing MPC formulations based on discrete-time control barrier functions (DCBFs) enforce safety through barrier constraints but typically result in computationally demanding nonlinear programming. To address this challenge, we construct a DCBF-augmented dynamical system and employ Koopman operator theory to lift the nonlinear dynamics into a higher-dimensional space where both the system dynamics and the barrier function admit a linear predictor representation. This enables the transformation of the nonlinear safety-constrained MPC problem into a quadratic program (QP). To improve feasibility while preserving safety, a relaxation mechanism with slack variables is introduced for the barrier constraints. The resulting approach combines the modeling capability of Koopman operators with the computational efficiency of QP. Numerical simulations on a navigation task for a robot with nonlinear dynamics demonstrate that the proposed framework achieves safe trajectory generation and efficient real-time control.

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Shuo Liu, Liang Wu, Dawei Zhang, Jan Drgona, Calin. A. Belta. 2026-03-22. Koopman-Based Linear MPC for Safe Control using Control Barrier Functions. https://arxiv.org/abs/2603.21070

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