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

• URL: http://arxiv.org/abs/2603.18503v1
• Date: Thu, 19 Mar 2026 05:23:21 GMT
• Title: Computationally Efficient Density-Driven Optimal Control via Analytical KKT Reduction and Contractive MPC
• Abstract summary: Efficient coordination for collective spatial distribution is a fundamental challenge in multi-agent systems.<n>We propose an analytical structural reduction that transforms the T-horizon KKT system into a condensed quadratic program (QP)<n>This formulation achieves O(T) linear scalability, significantly reducing the online computational burden compared to conventional O(T3) approaches.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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