Scaled consensus problem for multi-agent systems with semi-Markov switching topologies: A view from the probability |
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| Authors: | Xing Guo Jinling Liang Jianquan Lu |
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| Institution: | 1. School of Information Science and Engineering, Southeast University, Nanjing 210096, China;2. School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China;3. School of Mathematics, Southeast University, Nanjing 210096, China;1. College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi 435002, China;2. School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China;1. School of Automation, Beijing Institute of Technology, Beijing 100081, China;2. School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China;1. School of Computer Science and Technology, Anhui University of Technology, Ma’anshan 243002, China;2. School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong 252059, China;3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;4. School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243002, China;1. Faculty of Science, Yibin University, Yibin, Sichuan 644000, China;2. College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China;3. School of Mathematical and Statistics, Southwest University, Chongqing 400715, China;4. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;1. School of Automation, Southeast University, Nanjing 210096, China;2. Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Nanjing 210096, China |
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| Abstract: | This paper investigates the stochastic scaled consensus problem for multi-agent systems with semi-Markov switching topologies. Sufficient conditions are established to guarantee the addressed system to realize the scaled consensus with probability one, which means that all agents’ states almost surely reach a dictated proportion. Here, the semi-Markov process concerned is much more general than those utilized in the recent literature, which can be characterized by two important factors: (1) the transition probability matrix, and (2) the polytropical distribution functions of sojourn times. In addition, pinning scaled consensus protocol is designed by employing the pinning control technique, where only the root nodes of the union set of all the topologies are chosen to be pinned, and the final desired state value of the considered system can be realized with probability one. Finally, numerical simulations are provided to illustrate validity of the obtained main results. |
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