Adaptive decentralized control for a class of interconnected nonlinear systems via backstepping approach and graph theory

Abstract This paper is concerned with the adaptive decentralized control problem for a class of interconnected nonlinear systems, where the interconnections are assumed to be unknown and completely nonlinear. In addition, the interconnections and their bounds are allowed to contain the states of all subsystems. The main contribution is that, a strictly decentralized control scheme with compensation mechanism is developed to achieve the desirable tracking performance. More specifically, a smooth switching function is introduced to construct adaptive control laws, where the compensation mechanism is activated only if the immediate variable involved in the backstepping design exceeds a given constant, otherwise it will be turned-off. Furthermore, by combining graph theory and Lyapunov analysis method, it is proved that all the signals of the resulting closed-loop system are globally bounded, and the tracking errors of subsystems exponentially converge to a compact set, whose radius is adjustable by choosing different controller design parameters. Finally, the effectiveness of the proposed adaptive decentralized control scheme is illustrated with a simulated example.

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

[2]  Xudong Ye,et al.  Decentralized Adaptive Stabilization of Large-Scale Nonlinear Time-Delay Systems With Unknown High-Frequency-Gain Signs , 2011, IEEE Transactions on Automatic Control.

[3]  Anthony J. Calise,et al.  Coordinated decentralized adaptive output feedback control of interconnected systems , 2004, Proceedings of the 2004 American Control Conference.

[4]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[5]  Lin Shi,et al.  Decentralized adaptive controller design for large-scale systems with higher order interconnections , 1992 .

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

[7]  Wei Wang,et al.  Decentralized adaptive backstepping stabilization of interconnected systems with dynamic input and output interactions , 2009, Autom..

[8]  Michael Y. Li,et al.  Global-stability problem for coupled systems of differential equations on networks , 2010 .

[9]  Weisheng Chen,et al.  Fuzzy-approximation-based global adaptive control for uncertain strict-feedback systems with a priori known tracking accuracy , 2015, Fuzzy Sets Syst..

[10]  Prashanth Krishnamurthy,et al.  Decentralized control and disturbance attenuation for large-scale nonlinear systems in generalized output-feedback canonical form , 2003, Autom..

[11]  Francis Eng Hock Tay,et al.  Barrier Lyapunov Functions for the control of output-constrained nonlinear systems , 2009, Autom..

[12]  Yan Lin,et al.  Nonlinear decentralized control of large-scale systems with strong interconnections , 2014, Autom..

[13]  Shengyuan Xu,et al.  Neural-Network-Based Decentralized Adaptive Output-Feedback Control for Large-Scale Stochastic Nonlinear Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[15]  Lihua Xie,et al.  Decentralized stabilization of a class of interconnected stochastic nonlinear systems , 2000, IEEE Trans. Autom. Control..

[16]  Marios M. Polycarpou,et al.  Distributed Fault Accommodation for a Class of Interconnected Nonlinear Systems With Partial Communication , 2011, IEEE Transactions on Automatic Control.

[17]  Gongsheng Huang,et al.  Global decentralized robust stabilization for interconnected uncertain nonlinear systems with multiple inputs , 2001, Autom..

[18]  Yongming Li,et al.  Observer-Based Adaptive Decentralized Fuzzy Fault-Tolerant Control of Nonlinear Large-Scale Systems With Actuator Failures , 2014, IEEE Transactions on Fuzzy Systems.

[19]  Srdjan S. Stankovic,et al.  Robust stabilization of nonlinear interconnected systems by decentralized dynamic output feedback , 2009, Syst. Control. Lett..

[20]  Junmin Li,et al.  Decentralized Output-Feedback Neural Control for Systems With Unknown Interconnections , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[21]  Masayoshi Tomizuka,et al.  Decentralized robust control of mechanical systems , 2000, IEEE Trans. Autom. Control..

[22]  Mariesa L. Crow,et al.  Decentralized Dynamic Surface Control of Large-Scale Interconnected Systems in Strict-Feedback Form Using Neural Networks With Asymptotic Stabilization , 2011, IEEE Transactions on Neural Networks.

[23]  Zhong-Ping Jiang,et al.  Decentralized disturbance attenuating output-feedback trackers for large-scale nonlinear systems , 2002, Autom..

[24]  Donald T. Gavel,et al.  Decentralized adaptive control: structural conditions for stability , 1989 .

[25]  Kevin M. Passino,et al.  Decentralized adaptive control of nonlinear systems using radial basis neural networks , 1999, IEEE Trans. Autom. Control..

[26]  Bing Chen,et al.  Novel adaptive neural control design for nonlinear MIMO time-delay systems , 2009, Autom..

[27]  Zhong-Ping Jiang,et al.  Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems , 2007, Autom..

[28]  Kumpati S. Narendra,et al.  Exact output tracking in decentralized adaptive control systems , 2002, IEEE Trans. Autom. Control..

[29]  Jin Bae Park,et al.  Neural-Network-Based Decentralized Adaptive Control for a Class of Large-Scale Nonlinear Systems With Unknown Time-Varying Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).