Controlling Swarms toward Flocks and Mills

Carrillo, José A.; Kalise, Dante; Rossi, Francesco; Trélat, Emmanuel

doi:10.1137/21m1404314

Cited by 8 publications

(3 citation statements)

References 56 publications

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“…Agent-based models are a natural modelling framework to describe behaviour of a group of interacting entities obeying simple rules [69,27]. In this context, it is of great interest to explore the emergence of self-organizing patterns and collaborative behaviours among agents such as consensus, flocking, mills, etc.…”

Section: Optimal Control For Collective Dynamicsmentioning

confidence: 99%

Moment-Driven Predictive Control of Mean-Field Collective Dynamics

Albi¹,

Herty²,

Kalise³

et al. 2022

SIAM J. Control Optim.

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Feedback control synthesis for large-scale particle systems is reviewed in the framework of model predictive control (MPC). The high-dimensional character of collective dynamics hampers the performance of traditional MPC algorithms based on fast online dynamic optimization at every time step. Two alternatives to MPC are proposed. First, the use of supervised learning techniques for the offline approximation of optimal feedback laws is discussed. Then, a procedure based on sequential linearization of the dynamics based on macroscopic quantities of the particle ensemble is reviewed. Both approaches circumvent the online solution of optimal control problems enabling fast, real-time, feedback synthesis for large-scale particle systems. Numerical experiments assess the performance of the proposed algorithms.

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Section: Optimal Control For Collective Dynamicsmentioning

confidence: 99%

Moment-Driven Predictive Control of Mean-Field Collective Dynamics

Albi¹,

Herty²,

Kalise³

et al. 2022

SIAM J. Control Optim.

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show abstract

“…In 2019, Jia et al [10] introduced a hierarchical mechanism to the classical Vicsek model, proposing a hierarchical flocking model to explain the collaborative behaviors of specific agents. It is worth noting that the existing research on swarm control in multi-agent systems mainly focuses on integer-order dynamics, such as first-order dynamics [11,12] and second-order dynamics [13,14], while studies based on fractional-order dynamics are relatively scarce. Fractional calculus has been widely applied in natural sciences and engineering fields, such as linear and nonlinear dynamics, intelligent algorithm optimization, and characterizing the internal structures of complex functions.…”

Section: Introductionmentioning

confidence: 99%

A Discrete-Time Fractional-Order Flocking Control Algorithm of Multi-Agent Systems

Chen,

He,

Han

et al. 2024

Fractal Fract

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In this paper, a discrete-time fractional flocking control algorithm of multi-agent systems is put forward to address the slow convergence issue of multi-agent systems. Firstly, by introducing Grünwald-Letnikov (G-L) fractional derivatives, the algorithm allows agents to utilize historical information when updating their states. Secondly, based on the Lyapunov stability theory, the convergence of the algorithm is proven. Finally, simulations are conducted to verify the effectiveness of the proposed algorithm. Comparisons are made between the proposed algorithm and other methods. The results show that the proposed algorithm can effectively improve the convergence speed of multi-agent systems.

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“…Without aiming at full exhaustivity, we point the reader to the manuscripts [26,40,52,54] for various existence and qualitative regularity results on deterministic mean-field optimal control problems, as well as to the following broad series of works dealing with optimality conditions, either in the form of Pontryagin's maximum principle [17,19,20,22,25,75,76] or of Hamilton-Jacobi-Bellman equations [12,41,66]. We also mention the references [2,34,39,74] which propose astute control strategies to stir collective systems towards specific asymptotic patterns, and finally [1,20,29,30] for general numerical methods in the context of mean-field optimal control.…”

Section: Introductionmentioning

confidence: 99%

Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces

Bonnet

Frankowska

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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In this article, we derive necessary and sufficient conditions for the existence of solutions to stateconstrained continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in time. These latter are based on fine investigations of the infinitesimal behaviour of the underlying reachable sets, through which we show that up to a negligible set of times, every admissible velocity of the inclusion can be approximately realised as the metric derivative of a solution of the dynamics, and vice versa. Building on these results, we are able to establish necessary and sufficient geometric conditions for the viability and invariance of stationary and time-dependent constraints, which involve a suitable notion of contingent cones in Wasserstein spaces, presented in ascending order of generality. We then close the article by exhibiting two prototypical examples of constraints sets appearing in applications for which one can compute relevant subfamilies of contingent directions.

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Controlling Swarms toward Flocks and Mills

Cited by 8 publications

References 56 publications

Moment-Driven Predictive Control of Mean-Field Collective Dynamics

Moment-Driven Predictive Control of Mean-Field Collective Dynamics

A Discrete-Time Fractional-Order Flocking Control Algorithm of Multi-Agent Systems

Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces

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