Bipartite coordination problems on networks of multiple mobile agents

Bipartite tracking consensus of linear multi‐agent systems with a dynamic leader under signed digraph

“…In the multi‐agent system, an agent is called a leader if it does not receive information from other agents, while a follower if it can obtain the information from its neighbours. Lemma 1 The signed graph is structurally balanced if and only if there is a diagonal matrix , where and , such that has all non‐negative entries [33, 34]. …”

“…Lemma 3 For the non‐singular M‐matrix , there is a positive definite matrix [47], such that where Remark 1 Assumptions 1–3 are quite standard assumptions for the problem of bipartite tracking consensus of linear multi‐agent systems with a dynamic leader. Note that, Assumption 1 is standard for the solvability of the bipartite consensus problem of multi‐agent systems, and it is thus reasonable to state it in this paper as in [33–43]. Assumption 2 is commonly used in the literature to guarantee that there exist positive definite matrix solutions to the matrix inequalities (8) and (24), which is further used for feedback gain design.…”

“…In [33], bipartite consensus, which means that the states of the agents converge to a final state with the same magnitude but opposite sign, was introduced under a structurally balanced signed graph. Then, there has been a surge of attention given to the research of bipartite consensus of multi‐agent systems [34–43], because of its theoretical significance and potential applications. In [35], the interval bipartite consensus was introduced, and it was shown that a multi‐agent system can reach interval bipartite consensus when the signed digraph contains a directed spanning tree.…”

Adaptive bipartite consensus control of high‐order multiagent systems on coopetition networks

“…Contrary to consensus control, bipartite consensus control enables all agents to reach a final state with identical magnitude but opposite sign through cooperative and competitive interactions. [6][7][8][9][10] It is an extremely effective control strategy in those scenarios where cooperation and competition coexist among agents.…”

“…For cooperative-competitive multiagent systems with high-order agent dynamics, a static state-feedback controller was proposed in the work of Valcher and Misra, 7 and a dynamic output feedback controller was given in the work of Zhang and Chen 20 to guarantee bipartite consensus. A state-feedback controller was designed for a high-order multiagent system with input saturation in the work of Qin et al 21 An iterative learning control algorithm was provided for all agents to reach bipartite consensus on a reference trajectory in the work of Meng et al 9 Adaptive laws of time-varying coupling weights were proposed to solve a sign-consensus problem of linear multiagent systems in the work of Jiang et al 22 Some connectivity conditions were provided for bipartite consensus of discrete-time multiagent systems with switching networks in the work of Meng et al 23 An adaptive control protocol was designed to realize an interventional bipartite consensus for high-order multiagent systems with unknown disturbances in the work of Wu et al 10 Although many advances have been reported on the bipartite consensus problem, some challenging issues remain unresolved. For instance, the existing bipartite consensus strategies generally rely on some global information of the interaction topologies associated with multiagent systems, and thus, they are essentially not fully distributed.…”