Decentralized adaptive control of nonlinear large‐scale pure‐feedback interconnected systems with time‐varying delays

Abstract

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. DECENTRALIZED ADAPTIVE CONTROL 25 models be known exactly or the unknown nonlinear functions can be linearly parameterized. These control methods will be invalid, if the knowledge on nonlinear dynamics is not available.Recently, to overcome this limitation, many fuzzy logic systems (FLSs) or neural networks (NNs) control strategies for nonlinear systems have been proposed (see [10][11][12][13][14][15][16][17][18][19] with time delays or not), based on the reason that FLSs or NNs are universal approximators and have the ability to approximate the nonlinear functions. Although these approaches do not require nonlinear dynamic model to be known exactly or the unknown nonlinear functions to be linearly parameterized and still can achieve a good control performance, they are applied only to a relatively simple class of single nonlinear system. For large-scale systems, as is well known, because of the difficulties to deal with interconnections and the difficulties inherent in nonlinear subsystems, the decentralized control scheme designing with FLSs or NNs is still a challenging problem. Inspired by this challenge, many adaptive decentralized NN or fuzzy backstepping control approaches have been investigated for uncertain nonlinear systems [20][21][22][23][24][25][26].Although the approximation-based adaptive decentralized backstepping control approaches can overcome the difficulties that nonlinear systems do not satisfy the matching conditions and unknown nonlinear functions cannot be linearly parameterized, the backstepping design re...

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