Das, Abhijit; Lewis, Frank L. Distributed adaptive control for synchronization of unknown nonlinear networked systems. (English) Zbl 1205.93045 Automatica 46, No. 12, 2014-2021 (2010). Summary: 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. Cited in 138 Documents MSC: 93B51 Design techniques (robust design, computer-aided design, etc.) 93C40 Adaptive control/observation systems 93D30 Lyapunov and storage functions Keywords:nonlinear multiagent systems; distributed adaptive control; synchronization; consensus; networked systems PDFBibTeX XMLCite \textit{A. Das} and \textit{F. L. Lewis}, Automatica 46, No. 12, 2014--2021 (2010; Zbl 1205.93045) Full Text: DOI References: [1] Bernstein, D., Matrix mathematics (2005), Princeton Univ. Press: Princeton Univ. Press NJ [2] Chopra, N.; Spong, M. W., On exponential synchronization of kuramoto oscillators, IEEE Transactions on Automatic Control, 54, 2, 353-357 (2009) · Zbl 1367.34076 [3] Chopra, N.; Spong, M. 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