Computationally Efficient Density-Driven Optimal Control via Analytical KKT Reduction and Contractive MPC
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912973811875840 |
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| author | Martinez, Julian Lee, Kooktae |
| author_facet | Martinez, Julian Lee, Kooktae |
| contents | Efficient coordination for collective spatial distribution is a fundamental challenge in multi-agent systems. Prior research on Density-Driven Optimal Control (D2OC) established a framework to match agent trajectories to a desired spatial distribution. However, implementing this as a predictive controller requires solving a large-scale Karush-Kuhn-Tucker (KKT) system, whose computational complexity grows cubically with the prediction horizon. To resolve this, we propose an analytical structural reduction that transforms the T-horizon KKT system into a condensed quadratic program (QP). This formulation achieves O(T) linear scalability, significantly reducing the online computational burden compared to conventional O(T^3) approaches. Furthermore, to ensure rigorous convergence in dynamic environments, we incorporate a contractive Lyapunov constraint and prove the Input-to-State Stability (ISS) of the closed-loop system against reference propagation drift. Numerical simulations verify that the proposed method facilitates rapid density coverage with substantial computational speed-up, enabling long-horizon predictive control for large-scale multi-agent swarms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18503 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computationally Efficient Density-Driven Optimal Control via Analytical KKT Reduction and Contractive MPC Martinez, Julian Lee, Kooktae Optimization and Control Multiagent Systems Robotics Efficient coordination for collective spatial distribution is a fundamental challenge in multi-agent systems. Prior research on Density-Driven Optimal Control (D2OC) established a framework to match agent trajectories to a desired spatial distribution. However, implementing this as a predictive controller requires solving a large-scale Karush-Kuhn-Tucker (KKT) system, whose computational complexity grows cubically with the prediction horizon. To resolve this, we propose an analytical structural reduction that transforms the T-horizon KKT system into a condensed quadratic program (QP). This formulation achieves O(T) linear scalability, significantly reducing the online computational burden compared to conventional O(T^3) approaches. Furthermore, to ensure rigorous convergence in dynamic environments, we incorporate a contractive Lyapunov constraint and prove the Input-to-State Stability (ISS) of the closed-loop system against reference propagation drift. Numerical simulations verify that the proposed method facilitates rapid density coverage with substantial computational speed-up, enabling long-horizon predictive control for large-scale multi-agent swarms. |
| title | Computationally Efficient Density-Driven Optimal Control via Analytical KKT Reduction and Contractive MPC |
| topic | Optimization and Control Multiagent Systems Robotics |
| url | https://arxiv.org/abs/2603.18503 |