Continuification Control of Large-Scale Multiagent Systems in a Ring

Abstract

In this paper, we propose a method to control large-scale multiagent systems swarming in a ring. Specifically, we use a continuification-based approach that transforms the microscopic, agent-level description of the system dynamics into a macroscopic, continuum-level representation, which we employ to synthesize a control action towards a desired distribution of the agents. The continuum-level control action is then discretized at the agent-level in order to practically implement it. To confirm the effectiveness and the robustness of the proposed approach, we complement theoretical derivations with a series of numerical simulations.

Continuification control of large-scale multiagent systems under limited sensing and structural perturbations

“…fulfilling initial and boundary conditions similar to (9). As shown in [14], such a choice ensures that the density ρ globally asymptotically converges to ρ d . Then, we recast the macroscopic controlled model ( 9) to include q as a control action on the velocity field, that is,…”

“…As in [14], we consider a group of N identical mobile agents moving in S. The dynamics of the i-th agent can be expressed as…”

“…where x i is the angular position of agent i on S, {x i , x j } π is the angular distance between agents i and j wrapped on S, u i is the velocity control input, and f : S → R is a periodic velocity interaction kernel modeling pairwise interactions between the agents [14].…”

“…Such an approach was used in [14] to control the distribution of a multiagent system swarming in a ring, leading to an effective control scheme for the multiagent system to achieve a desired distribution. Crucially, to prove convergence of the macroscopic collective dynamics towards the desired distribution, two key assumptions were made.…”

“…After providing some useful notation and mathematical preliminaries in Section II, we briefly recall the approach of [14] in Section III. Then, we assess the robustness properties of the continuification control approach in Sections IV and V. Finally, in Section VI, we show some preliminary results on the use of an additional integral action at the macroscopic level to improve the robustness of the microscopic dynamics, in the presence of perturbations or limited sensing.…”