Control processes

Decentralized control algorithms for a group of mobile agents on a line under distributed communication delay

A. Yu. Aleksandrov, S. B. Ruzin

St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

Abstract: A group of mobile agents on a straight line is studied, the dynamics of which are modeled by second-order integrators. It is assumed that there is a distributed delay in the communication channels between agents. In addition, the case of a switching network topology is considered, and the switching law may be unknown. Decentralized protocols are constructed that ensure both uniform and nonlinear-uniform (uniform with respect to some function) distributions of agents on a given segment of the straight line. It is proved that the convergence of agents to the required distributions is guaranteed for any switching law of connections. To obtain these results, methods of the theory of positive systems, a special approach to the decomposition of mechanical systems, and the Lyapunov direct method are used. Numerical modeling is carried out, confirming the established theoretical conclusions.

Keywords: network control, mobile agents, double integrators, distributed delay, switchings, Lyapunov — Krasovskii functional.

UDC: 517.977.1

MSC: 93C35

Received: October 23, 2024
Accepted: December 17, 2024

DOI: 10.21638/spbu10.2025.110