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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2605.00395 |
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| _version_ | 1866914524195454976 |
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| author | Yu, Jiguang |
| author_facet | Yu, Jiguang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00395 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Controlling the Swarm: Sparse Actuation and Collision Avoidance under Stochastic Delay Yu, Jiguang Optimization and Control 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. |
| title | Controlling the Swarm: Sparse Actuation and Collision Avoidance under Stochastic Delay |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.00395 |