Koopman-Based Linear MPC for Safe Control using Control Barrier Functions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914432399966208 |
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| author | Liu, Shuo Wu, Liang Zhang, Dawei Drgona, Jan Belta, Calin. A. |
| author_facet | Liu, Shuo Wu, Liang Zhang, Dawei Drgona, Jan Belta, Calin. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21070 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Koopman-Based Linear MPC for Safe Control using Control Barrier Functions Liu, Shuo Wu, Liang Zhang, Dawei Drgona, Jan Belta, Calin. A. Systems and Control 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. |
| title | Koopman-Based Linear MPC for Safe Control using Control Barrier Functions |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2603.21070 |