Distributed adaptive control for synchronization of unknown nonlinear networked systems |
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| Authors: | Abhijit Das Frank L. Lewis |
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| Affiliation: | 1. School of Automation, Southeast University, Nanjing 210096, China;2. Department of Mathematics, Southeast University, Nanjing 210096, China;3. Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China;4. School of Electrical Engineering, Southeast University, Nanjing 210096, China;5. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;6. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. School of Marine Engineering, Dalian Maritime University, China;2. School of Electrical Engineering, Liaoning University of Technology, China;1. Systems Engineering Department, KFUPM, P.O. 5067, Dhahran 31261, Saudi Arabia;2. Research Institute, The University of Texas at Arlington, TX 76118, United States;1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, China;2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China;2. School of Electrical and Electronic Engineering, Nanyang Technological University, 639798 Singapore, Singapore;3. UTA Research Institute, University of Texas at Arlington, Fort Worth, Texas, USA;4. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China |
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| Abstract: | This paper is concerned with synchronization of distributed node dynamics to a prescribed target or control node dynamics. A design method is presented for adaptive synchronization controllers for distributed systems having non-identical unknown nonlinear dynamics, and for a target dynamics to be tracked that is also nonlinear and unknown. The development is for strongly connected digraph communication structures. A Lyapunov technique is presented for designing a robust adaptive synchronization control protocol. The proper selection of the Lyapunov function is the key to ensuring that the resulting control laws thus found are implementable in a distributed fashion. Lyapunov functions are defined in terms of a local neighborhood tracking synchronization error and the Frobenius norm. The resulting protocol consists of a linear protocol and a nonlinear control term with adaptive update law at each node. Singular value analysis is used. It is shown that the singular values of certain key matrices are intimately related to structural properties of the graph. |
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