Event-triggered Pinning Bipartite Tracking Consensus of the Multi-agent System Subject to Input Saturation
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Event-triggered Pinning Bipartite Tracking Consensus of the Multi-agent System Subject to Input Saturation Hai-Yun Gao and Ai-Hua Hu* Abstract: This paper focuses on the bipartite tracking consensus problem of the multi-agent system with cooperative-competitive interactions. In order to save resources, an event-triggered pinning scheme subjected to input saturation is designed. Suppose that the signed graph representing cooperative-competitive interactions is structurally balanced, and the initial states for the agents belong to the specified ellipsoid. By using Lyapunov theory and linear matrix inequality (LMI) techniques, some sufficient conditions are derived to ensure that the bipartite tracking consensus of the system under event-triggered pinning control can be achieved. Moreover, the bipartite tracking consensus of system with Lipschitz nonlinear dynamics is also investigated, and Zeno behavior can be excluded. Subsequently, numerical examples are provided to illustrate the effectiveness of the obtained results. Keywords: Bipartite tracking consensus, event-triggered scheme, input saturation, nonlinear dynamics, pinning control.
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INTRODUCTION
Recent years, distributed coordinated control of multiagent systems and synchronization of complex networks [1] has been extensively studied. One of the hottest topics is the consensus problem [2–5], which means that agents in a network can attain a common target through designing reasonable protocols. However, with the increase of the scale and complexity, only one target cannot meet the requirements of a system. Some scholars have proposed the definition of the group consensus [6]. The multi-agent system contains multiple sub-systems, and all agents in the same sub-system converge to the identical value, while agents in the different sub-systems aggregate to non-identical values. Furthermore, in many real-world scenarios, there is a special consensus phenomenon, where all agents can ultimately reach the final values with identical magnitude but opposite sign through the cooperative-competitive interactions [7]. This phenomenon can be seen as bipartite consensus, and it is a special case of group consensus. Actually, bipartite consensus is very universal in the field of nature or engineering. For instance, in an economic system, when companies rival for customer resources, there will be a duopolistic regime [8]. In a multi-robot system, robots demand to work with teammates and compete with the antagonistic robots. And in a biological system, when genes
cooperate with each other, the genes can be taken as activators. When the interaction between genes is competitive, the genes are called inhibitors. Obviously, it is very interesting and necessary to study bipartite consensus. More and more attention has been paid to the bipartite consensus problem for multi-agent systems, and a large amount of work has been done [7–13]. Deng et al. addressed the fixed-time bipartite consensus for multi-agent systems sub
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