Controlling the Swarm: Sparse Actuation and Collision Avoidance under Stochastic Delay

TL;DR

This paper develops a rigorous framework for controlling stochastic delayed multi-agent swarms with sparse actuation, addressing collision avoidance and resource efficiency.

Contribution

It introduces a novel mathematical approach to ensure well-posedness and optimal control in complex stochastic swarm systems with limited actuation.

Findings

Sparse leader actuation reduces control effort significantly.

Adding more actuation is not always optimal in delayed stochastic swarms.

Non-monotone sensitivity to leader density affects control strategies.

Abstract

Classical flocking models demonstrate how local interactions generate emergent order, but real-world multi-agent deployments are bound by severe constraints: limited actuator availability, heterogeneous communication latencies, and environmental noise. In this talk, we present a unified finite-N framework that tackles the interplay of these exact mechanisms. We study a delayed stochastic leader-follower particle system featuring topological communication, singular repulsion, and bounded sparse leader actuation. A central challenge in such systems is mathematical well-posedness, as discontinuous communication laws and singular repulsions clash with standard strong Ito frameworks. We resolve this by introducing an augmented Lyapunov functional that simultaneously enforces a strict collision barrier and closes a uniform Gronwall estimate. Building on this rigorous foundation, we formulate a free-terminal-time, chance-constrained optimal control problem. We show that temporally sparse, bang-off-bang leader actuation not only drastically reduces control effort compared to continuous baselines, but also reveals non-monotone sensitivities to leader density. Ultimately, we demonstrate that in delayed stochastic swarms, adding more direct actuation is not strictly optimal -- highlighting a highly non-trivial resource allocation paradox in cooperative control.