Backstepping-based decentralized tracking control for a class of interconnected stochastic nonlinear systems coupled via a directed graph

Abstract This paper studies the decentralized tracking control problem for a class of interconnected stochastic nonlinear systems defined on a directed graph, where the interconnections are allowed to include the states of each subsystems. The main contributions are that a new strictly decentralized control method is proposed to acquire the desired tracking performance, and a modified compensation mechanism is presented to address the state-dependent interconnections. Furthermore, by using quartic Lyapunov functions and graph theory, it is proved that the signals of the resulting closed-loop system are globally bounded in probability, and the tracking errors converge to a compact set, whose radius can be adjusted by choosing different controller design parameters. Finally, two examples are used to illustrate the effectiveness of the proposed method.

[1]  Bing Chen,et al.  Neural-Based Adaptive Output-Feedback Control for a Class of Nonstrict-Feedback Stochastic Nonlinear Systems , 2015, IEEE Transactions on Cybernetics.

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

[3]  James Lam,et al.  Robust integral sliding mode control for uncertain stochastic systems with time-varying delay , 2005, Autom..

[4]  Peng Shi,et al.  Adaptive Tracking for Stochastic Nonlinear Systems With Markovian Switching $ $ , 2010, IEEE Transactions on Automatic Control.

[5]  Daniel W. C. Ho,et al.  A note on the robust stability of uncertain stochastic fuzzy systems with time-delays , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[6]  Feifei Yang,et al.  Decentralized adaptive neural control for interconnected stochastic nonlinear delay-time systems with asymmetric saturation actuators and output constraints , 2018, J. Frankl. Inst..

[7]  Shaocheng Tong,et al.  Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults , 2017, IEEE Transactions on Cybernetics.

[8]  Wuquan Li,et al.  Output Tracking of Stochastic High-Order Nonlinear Systems with Markovian Switching , 2013, IEEE Transactions on Automatic Control.

[9]  Guang-Hong Yang,et al.  Adaptive Reliable Coordination Control for Linear Agent Networks With Intermittent Communication Constraints , 2018, IEEE Transactions on Control of Network Systems.

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

[11]  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).

[12]  Li Xu,et al.  Decentralized adaptive output-feedback controller design for stochastic nonlinear interconnected systems , 2012, Autom..

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

[14]  Yeong-Chan Chang,et al.  Robust tracking control for nonlinear MIMO systems via fuzzy approaches , 2000, Autom..

[15]  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..

[16]  Guang-Hong Yang,et al.  Neural-Network-Based Adaptive Decentralized Fault-Tolerant Control for a Class of Interconnected Nonlinear Systems , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Hongye Su,et al.  Adaptive Backstepping Control for a Class of Nonlinear Systems With Non-Triangular Structural Uncertainties , 2017, IEEE Transactions on Automatic Control.

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

[19]  Tianping Zhang,et al.  Decentralized adaptive fuzzy output feedback control of stochastic nonlinear large-scale systems with dynamic uncertainties , 2015, Inf. Sci..

[20]  Weihua Gui,et al.  Passivity-Based Asynchronous Sliding Mode Control for Delayed Singular Markovian Jump Systems , 2018, IEEE Transactions on Automatic Control.

[21]  Wei Wang,et al.  Hierarchical Decomposition Based Consensus Tracking for Uncertain Interconnected Systems via Distributed Adaptive Output Feedback Control , 2016, IEEE Transactions on Automatic Control.

[22]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[23]  Xin-Ping Guan,et al.  Decentralised adaptive control for a class of stochastic switched interconnected nonlinear systems , 2016, Int. J. Syst. Sci..

[24]  T. Başar,et al.  Backstepping Controller Design for Nonlinear Stochastic Systems Under a Risk-Sensitive Cost Criterion , 1999 .

[25]  Shengyuan Xu,et al.  Observer-Based Adaptive Neural Network Control for Nonlinear Stochastic Systems With Time Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[26]  Dong Yue,et al.  Decentralized Adaptive Event-Triggered $H_\infty$ Filtering for a Class of Networked Nonlinear Interconnected Systems , 2019, IEEE Transactions on Cybernetics.

[27]  Jie Tian,et al.  Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization , 2009, Autom..

[28]  Ramazan Coban.  Backstepping integral sliding mode control of an electromechanical system , 2017 .

[29]  Yumei Sun,et al.  Adaptive neural control for a class of stochastic nonlinear systems by backstepping approach , 2016, Inf. Sci..

[30]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[32]  Yan Lin,et al.  Decentralized adaptive tracking control for a class of interconnected nonlinear time-varying systems , 2015, Autom..

[33]  Mohamed Hamdy,et al.  Adaptive neural decentralized control for strict feedback nonlinear interconnected systems via backstepping , 2012, Neural Computing and Applications.

[34]  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.

[35]  Ramazan Coban.  Dynamical adaptive integral backstepping variable structure controller design for uncertain systems and experimental application , 2017 .

[36]  D. West.  Introduction to Graph Theory , 1995 .

[37]  Hai-Bo Ji,et al.  Adaptive output-feedback tracking of stochastic nonlinear systems , 2006, IEEE Trans. Autom. Control..

[38]  Guang-Hong Yang,et al.  Distributed reliable H∞ consensus control for a class of multi‐agent systems under switching networks: A topology‐based average dwell time approach , 2016 .

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

[40]  Ligang Wu,et al.  Fault Detection Filtering for Nonhomogeneous Markovian Jump Systems via a Fuzzy Approach , 2018, IEEE Transactions on Fuzzy Systems.

[41]  Dong Yue,et al.  tracking control of nonlinear networked systems with a novel adaptive event-triggered communication scheme , 2017 .

[42]  Guang-Hong Yang,et al.  Adaptive decentralized control for a class of interconnected nonlinear systems via backstepping approach and graph theory , 2017, Autom..

[43]  Xiaoping Liu,et al.  Robust Adaptive Neural Tracking Control for a Class of Stochastic Nonlinear Interconnected Systems , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[44]  Gang Tao,et al.  Adaptive Fault-Tolerant Control of Uncertain Nonlinear Large-Scale Systems With Unknown Dead Zone , 2016, IEEE Transactions on Cybernetics.

[45]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[46]  Wei Xing Zheng,et al.  ${\cal L}_{2}$– ${\cal L}_{\infty}$ Control of Nonlinear Fuzzy ItÔ Stochastic Delay Systems via Dynamic Output Feedback , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[47]  Weihua Gui,et al.  Event-Based Fault Detection Filtering for Complex Networked Jump Systems , 2018, IEEE/ASME Transactions on Mechatronics.