Asymptotic behavior and control of a "guidance by repulsion" model

Ko D, Zuazua Iriondo E (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Mathematical Models & Methods in Applied Sciences World Scientific Publishing

DOI: 10.1142/S0218202520400047

Abstract

We model and analyze a guiding problem, where the drivers try to steer the evaders' positions toward a target region while the evaders always try to escape from drivers. This problem is motivated by the guidance-by-repulsion model [R. Escobedo, A. Ibañez and E. Zuazua, Optimal strategies for driving a mobile agent in a "guidance by repulsion" model, Commun. onlinear Sci. umer. Simul. 39 (2016) 58-72] where the authors answer how to control the evader's position and what is the optimal maneuver of the driver. First, we analyze well posedness and behavior of the one-driver and one-evader model, assuming of the same friction coefficients. From the long-time behavior, the exact controllability is proved in a long enough time horizon. Then, we extend the model to the multi-driver and multi-evader case. We assumed three interaction rules in the context of collective behavior models: flocking between evaders, collision avoidance between drivers and repulsive forces between drivers and evaders. These interactions depend on the relative distances, and each agent is assumed to be undistinguishable and obtained an averaged effect from the other individuals. In this model, we develop numerical simulations to systematically explore the nature of controlled dynamics in various scenarios. The optimal strategies turn out to share a common pattern to the one-driver and one-evader case: the drivers rapidly occupy the position behind the target, and want to pursuit evaders in a straight line for most of the time. Inspired by this, we build a feedback strategy which stabilizes the direction of evaders.

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

University of Deusto / Universidad de Deusto ES Spain (ES)

How to cite

APA:

Ko, D., & Zuazua Iriondo, E. (2020). Asymptotic behavior and control of a "guidance by repulsion" model. Mathematical Models & Methods in Applied Sciences. https://doi.org/10.1142/S0218202520400047

MLA:

Ko, Dongnam, and Enrique Zuazua Iriondo. "Asymptotic behavior and control of a "guidance by repulsion" model." Mathematical Models & Methods in Applied Sciences (2020).

BibTeX: Download