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Decentralized adaptive control of nonlinear large‐scale pure‐feedback interconnected systems with time‐varying delays
Author(s) -
He Chao,
Li Junmin,
Zhang Lin
Publication year - 2015
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2455
Subject(s) - backstepping , control theory (sociology) , bounded function , nonlinear system , artificial neural network , computer science , hyperbolic function , uniform boundedness , controller (irrigation) , mean value theorem (divided differences) , function (biology) , adaptive control , lyapunov function , strict feedback form , control (management) , mathematics , mathematical optimization , artificial intelligence , physics , fixed point theorem , evolutionary biology , pure mathematics , agronomy , biology , picard–lindelöf theorem , mathematical analysis , quantum mechanics
SUMMARY In this paper, an adaptive decentralized neural control problem is addressed for a class of pure‐feedback interconnected system with unknown time‐varying delays in outputs interconnections. By taking advantage of implicit function theorem and the mean‐value theorem, the difficulty from the pure‐feedback form is overcome. Under a wild assumption that the nonlinear interconnections are assumed to be bounded by unknown nonlinear functions with outputs, the difficulties from unknown interconnections are dealt with, by introducing continuous packaged functions and hyperbolic tangent functions, and the time‐varying delays in interconnections are compensated by Lyapunov–Krasovskii functional. Radial basis function neural network is used to approximate the unknown nonlinearities. Dynamic surface control is successfully extended to eliminate ‘the explosion of complexity’ problem in backstepping procedure. To reduce the computational burden, minimal learning parameters technique is successfully incorporated into this novel control design. A delay‐independent decentralized control scheme is proposed. With the adaptive neural decentralized control, only one estimated parameter need to be updated online for each subsystem. Therefore, the controller is more simplified than the existing results. Also, semiglobal uniform ultimate boundedness of all of the signals in the closed‐loop system is guaranteed. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme. Copyright © 2013 John Wiley & Sons, Ltd.