Abstract
In this paper, the consensus problem is investigated for a group of first-order agents in the cooperation–competition network, where agents can cooperate or even compete with each other, i.e., the elements in the coupling weight matrix of the graph can be either positive or negative. In order to solve this consensus problem, the whole network is firstly divided into two sub-networks, i.e., the cooperation sub-network and the competition sub-network, and then two kinds of time-delayed control schemes are designed in the competition sub-network. By combining the Lyapunov theory together with the synchronization manifold method, several effective sufficient conditions of consensus are provided without assuming that the interaction topology is strongly connected or contains a directed spanning tree, which means that the competition relationships could help the agents achieve consensus under the time-delayed control designed in the competition sub-network. Moreover, the results are also extended to the pure competition networks where all the elements in the weight matrices are either zeros or negative. Finally, some simulation examples are provided to validate the effectiveness of the theoretical analysis.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.