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

Fuente: arXiv
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Main Authors: Liu, Shuo, Wu, Liang, Zhang, Dawei, Drgona, Jan, Belta, Calin. A.
Format: Preprint
Published: 2026
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_version_ 1866914432399966208
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