Swarming Behavior of Multiple Euler–Lagrange Systems With Cooperation–Competition Interactions: An Auxiliary System Approach

TLDR

The study investigates the swarming behavior of multiple Euler–Lagrange systems that interact via cooperation and competition, with uncertain system parameters. An auxiliary system is introduced for each agent, eliminating the digon sign‑symmetry assumption, to analyze distributed stabilization and later consensus tracking using a pinning control strategy based on equi‑competition. Distributed stabilization is achieved when the cooperation subnetwork is strongly connected and auxiliary parameters are appropriately chosen, and illustrative examples confirm the approach’s effectiveness.

Abstract

In this paper, the swarming behavior of multiple Euler-Lagrange systems with cooperation-competition interactions is investigated, where the agents can cooperate or compete with each other and the parameters of the systems are uncertain. The distributed stabilization problem is first studied, by introducing an auxiliary system to each agent, where the common assumption that the cooperation-competition network satisfies the digon sign-symmetry condition is removed. Based on the input-output property of the auxiliary system, it is found that distributed stabilization can be achieved provided that the cooperation subnetwork is strongly connected and the parameters of the auxiliary system are chosen appropriately. Furthermore, as an extension, a distributed consensus tracking problem of the considered multiagent systems is discussed, where the concept of equi-competition is introduced and a new pinning control strategy is proposed based on the designed auxiliary system. Finally, illustrative examples are provided to show the effectiveness of the theoretical analysis.