Computationally Efficient Density-Driven Optimal Control via Analytical KKT Reduction and Contractive MPC

Abstract: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.

Optimization and Control (math.OC); Multiagent Systems (cs.MA); Robotics (cs.RO)

arXiv:2603.18503 [math.OC]

(or arXiv:2603.18503v2 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2603.18503 Focus to learn more arXiv-issued DOI via DataCite

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