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

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.

Guaranteed‐performance consensus tracking of singular multiagent systems with Lipschitz nonlinear dynamics and switching topologies

“…Remark 6. In accordance with (8), one can get that agent i is not influenced by the topology switching. The switched property of closed-loop system (13) is caused by the introduction of input signal u i (t), which contains the switching topology information a (t),i j .…”

“…Moreover, an assumption for dynamics (8) together with the definitions of guaranteed-performance leader-following consensus (or consensus tracking) and consensualization of nonlinear singular multiagent systems (8) are given herein. (8) is said to achieve guaranteed-performance consensus tracking if there exists a scalar J * such that it achieves consensus tracking, whereas the performance function (11) satisfies J p ≤ J * , where J * is said to be the guaranteed-performance cost.…”

“…Theorem 1. For scalars > 0, > 0 and > 0, multiagent systems (8) achieve consensus tracking by protocol 10 if there exist a symmetric matrix X and a nonsingular matrix Φ with appropriate dimensions such that the following LMIs hold:…”

“…The equivalent relationship between the consensus tracking of multiagent systems (8) and the admissibility for system (22) holds for the following two reasons. Firstly, in accordance with Definition 3, multiagent systems (8) achieves consensus tracking if the global consensus error system (19) is admissible. Secondly, system (22) is derived from system (19) via nonsingular transformation (22).…”

“…1 This is due not only to its wide applications in many fields such as formation control of unmanned surface vehicles, 2,3 information fusion of distributed sensor networks, 4 and attitude synchronization of multiple spacecrafts 5 but also to the theoretical interest and challenges on analyzing the complex global behaviors among a group of identical agents, which include rendezvous, 6 flocking, 7 and swarming. 8 In the area of distributed cooperative control of multiagent systems, consensus is considered as one of the most important and fundamental issues, which implies that the states or outputs of all agents reach an agreement by the designed protocol. 9 A multitude of results has been proposed by considering the consensus problem from different viewpoints, such as communication time-delays, 10 uncertain perturbations and exogenous disturbances, 11 and dynamically changing interaction topologies, 12 to name a few.…”