Stochastic leader-following consensus of discrete-time nonlinear multi-agent systems with multiplicative noises |
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| Institution: | 1. School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;2. School of Automation, China University of Geosciences, Wuhan 430074, China;3. Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China;1. Department of Applied Mathematics, Bharathiar University, Coimbatore 641046, India;2. Department of Communications and Networks Engineering, Prince Sultan University, Saudi Arabia;1. School of Automation Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China;2. SKLMSE lab, MOE Key Laboratory for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an 710049, China;3. Institute of Aero-engine, School of Mechanical Engineering, Xi’an Jiao Tong University, Xi’an 710049, China;1. College of Science, Hunan University of Technology, Zhuzhou 412000, Hunan, P. R. China;2. Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, P. R. China;3. The Mork Family Department of Chemical Engineering and Materials Science, Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089 USA;1. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China;2. Research Center of Semi-tensor Product of Matrices, Theory and Applications, Liaocheng University, Lianocheng, PR China;3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China;1. College of Data Science, Jiaxing University, Zhejiang 314001, China;2. Jiaxing NanHu University, Zhejiang 314001, China;3. School of Mathematics, Southeast University, Nanjing 211189, China;4. Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea;5. Department of Mathematics, Nazarbayev University, Nur-Sultan 010000, Kazakhstan |
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| Abstract: | This paper studies the stochastic leader-following consensus problem of discrete-time nonlinear multi-agent systems (MASs) with multiplicative noises. The measurement information obtained from agents’ neighbors is inevitably affected by communication uncertainties, where the multiplicative noise is one of the important communication uncertainties. Multiplicative noises together with the intrinsic nonlinear dynamics bring more difficulties in the consensus control design under the leader-following topology. To solve the problem, the parameter-dependent Lyapunov functions are constructed to analyze the consensus control of first-order and second-order MASs, respectively. Some sufficient conditions, explicitly related to control gains, intensity of multiplicative noises and the Lipschitz constant regarding nonlinear functions, are established for reaching the mean square (m.s.) and almost sure (a.s.) leader-following consensus. Specifically, the obtained conditions are some scalar inequalities, which are more convenient in engineering application. Numerical simulations are conducted to validate the theoretical results. |
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