Constraint horizon in model predictive control

Journal article

In this work, we propose a Model Predictive Control (MPC) formulation incorporating two distinct horizons: a prediction horizon and a constraint horizon. This approach enables a deeper understanding of how constraints influence key MPC properties such as suboptimality, without compromising recursive feasibility and constraint satisfaction. In this direction, our contributions are twofold. First, we provide a framework to estimate closed-loop optimality as a function of the number of enforced constraints. This is a generalization of existing results by considering partial constraint enforcement over the prediction horizon. Second, when adopting this general framework under the lens of safety-critical applications, our method improves conventional Control Barrier Function (CBF) based approaches. It mitigates myopic behaviour in Quadratic Programming (QP)-CBF schemes, and resolves compatibility issues between Control Lyapunov Function (CLF) and CBF constraints via the prediction horizon used in the optimization. We show the efficacy of the method via numerical simulations for a safety critical application.

Authors: do Nascimento, AA; Wang, H; Papachristodoulou, A; Margellos, K

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IEEE
• Journal: IEEE Control Systems Letters
• Publication date: 2025-06-16
• Acceptance date: 2025-06-01
• DOI: 10.1109/LCSYS.2025.3580355
• EISSN: 2475-1456
• Language: English
• Keywords: model predictive control; optimal control; constrained control; control barrier functions