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This paper introduces a computationally efficient Density-Driven Optimal Control (D2OC) method for multi-agent systems by analytically reducing the Karush-Kuhn-Tucker (KKT) system inherent in predictive control. They achieve linear O(T) scalability by transforming the T-horizon KKT system into a condensed quadratic program, a significant improvement over the conventional O(T^3) complexity. The method also incorporates a contractive Lyapunov constraint to guarantee Input-to-State Stability (ISS) in dynamic environments.
Unlock real-time control for massive multi-agent swarms: this method slashes computation from cubic to linear with horizon length, making long-horizon density-driven control practical.
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.
