Neural-Network-Based Decentralized Adaptive Control for a Class of Large-Scale Nonlinear Systems With Unknown Time-Varying Delays

A decentralized adaptive methodology is presented for large-scale nonlinear systems with model uncertainties and time-delayed interconnections unmatched in control inputs. The interaction terms with unknown time-varying delays are bounded by unknown nonlinear bounding functions related to all states and are compensated by choosing appropriate Lyapunov-Krasovskii functionals and using the function approximation technique based on neural networks. The proposed memoryless local controller for each subsystem can simply be designed by extending the dynamic surface design technique to nonlinear systems with time-varying delayed interconnections. In addition, we prove that all the signals in the closed-loop system are semiglobally uniformly bounded, and the control errors converge to an adjustable neighborhood of the origin. Finally, an example is provided to illustrate the effectiveness of the proposed control system.

[1]  Xin-Ping Guan,et al.  Output Feedback Stabilization for Time-Delay Nonlinear Interconnected Systems Using Neural Networks , 2008, IEEE Transactions on Neural Networks.

[2]  Tamer Basar,et al.  Decentralized risk-sensitive controller design for strict-feedback systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[3]  M. Polycarpou,et al.  Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators , 1998 .

[4]  P. Shi,et al.  Robust Decentralized Adaptive Control for Interconnected Systems With Time Delays , 2005 .

[5]  Jin Bae Park,et al.  Adaptive Dynamic Surface Control for Stabilization of Parametric Strict-Feedback Nonlinear Systems With Unknown Time Delays , 2007, IEEE Transactions on Automatic Control.

[6]  Petros A. Ioannou.  Decentralized adaptive control of interconnected systems , 1986 .

[7]  Cheng-Wu Chen,et al.  Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control , 2005, IEEE Trans. Fuzzy Syst..

[8]  Chih-Hong Lin,et al.  Robust H∞ controller design with recurrent neural network for linear synchronous motor drive , 2003, IEEE Trans. Ind. Electron..

[9]  Jun-Juh Yan.  Memoryless Adaptive Decentralized Sliding Mode Control for Uncertain Large-Scale Systems With Time-Varying Delays , 2003 .

[10]  H. Wu,et al.  Decentralized Stabilizing State Feedback Controllers for a Class of Large-Scale Systems Including State Delays in the Interconnections , 1999 .

[11]  James Lam,et al.  Decentralized Stabilization of Large-Scale Interconnected Time-Delay Systems , 1999 .

[12]  Jin Bae Park,et al.  Indirect adaptive control of nonlinear dynamic systems using self recurrent wavelet neural networks via adaptive learning rates , 2007, Inf. Sci..

[13]  P. P. Yip,et al.  Adaptive dynamic surface control : a simplified algorithm for adaptive backstepping control of nonlinear systems , 1998 .

[14]  Zhongzhi Hu,et al.  Decentralized stabilization of large scale interconnected systems with delays , 1994, IEEE Trans. Autom. Control..

[15]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: the smooth feedback case , 2002, IEEE Trans. Autom. Control..

[16]  Petros A. Ioannou,et al.  Adaptive Systems with Reduced Models , 1983 .

[17]  Ju H. Park,et al.  Robust Nonfragile Decentralized Controller Design for Uncertain Large-Scale Interconnected Systems With Time-Delays , 2002 .

[18]  S. Jain,et al.  Decentralized adaptive control of a class of large-scale interconnected nonlinear systems , 1997, IEEE Trans. Autom. Control..

[19]  P. Shi,et al.  Decentralized robust model reference adaptive control for interconnected time-delay systems , 2004, Proceedings of the 2004 American Control Conference.

[20]  Jin Bae Park,et al.  Adaptive Dynamic Surface Control of Flexible-Joint Robots Using Self-Recurrent Wavelet Neural Networks , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[21]  Swaroop Darbha,et al.  Dynamic surface control for a class of nonlinear systems , 2000, IEEE Trans. Autom. Control..

[22]  H. Wu,et al.  Decentralized Adaptive Robust State Feedback for Uncertain Large-Scale Interconnected Systems with Time Delays , 2005 .

[23]  Hansheng Wu,et al.  Decentralized adaptive robust control for a class of large-scale systems including delayed state perturbations in the interconnections , 2002, IEEE Trans. Autom. Control..

[24]  Cheng-Wu Chen,et al.  Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems , 2004, Math. Comput. Simul..

[25]  Kwang Y. Lee,et al.  Diagonal recurrent neural networks for dynamic systems control , 1995, IEEE Trans. Neural Networks.

[26]  Magdi S. Mahmoud,et al.  Robust Design of Stabilizing Controllers for Interconnected Time-delay Systems , 1998, Autom..

[27]  Petar V. Kokotovic,et al.  Decentralized adaptive control of interconnected systems with reduced-order models , 1985, Autom..

[28]  Dan Wang,et al.  Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form , 2005, IEEE Transactions on Neural Networks.

[29]  Keng Peng Tee,et al.  Approximation-based control of nonlinear MIMO time-delay systems , 2007, Autom..

[30]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[31]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[32]  Chih-Chiang Cheng,et al.  A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems , 2003, IEEE Trans. Autom. Control..

[33]  Gérard Dreyfus,et al.  Training wavelet networks for nonlinear dynamic input-output modeling , 1998, Neurocomputing.

[34]  C. Wen.  Decentralized adaptive regulation , 1994, IEEE Trans. Autom. Control..