SCIENCE CHINA Information Sciences, Volume 60, Issue 12: 120207(2017) https://doi.org/10.1007/s11432-017-9142-3

Decentralized backstepping adaptive output tracking of large-scale stochastic nonlinear systems

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  • ReceivedApr 28, 2017
  • AcceptedJun 15, 2017
  • PublishedNov 9, 2017


The problem of decentralized adaptive output tracking control of a class ofinterconnected stochastic nonlinear systems is considered. In the control design, decentralized state observers and backstepping techniques are applied.To eliminate the influences of interactions with other subsystems, a differentiable function is employed. It is shown that the designed local adaptivecontrollers can ensure that all the signals in the closed-loop system arebounded in probability. Furthermore, the tracking errors can be limited to asmall residual set around the origin in the fourth moment sense and can be adjusted by choosing suitable design parameters.


This work was supported by National Natural Science Foundation of China (Grant Nos. 61325014, 61374072).


[1] Bakule L. Decentralized control: An overview. Annu Rev Control, 2008, 32: 87-98 CrossRef Google Scholar

[2] Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans Automat Contr, 1991, 36: 1241-1253 CrossRef Google Scholar

[3] Arslan G, Ba?ar T. Decentralized risk-sensitive controller design for strict-feedback systems. Syst Control Lett, 2003, 50: 383-393 CrossRef Google Scholar

[4] Gavel D T, Siljak D D. Decentralized adaptive control: structural conditions for stability. IEEE Trans Automat Contr, 1989, 34: 413-426 CrossRef Google Scholar

[5] Guo Y, Jiang Z P, Hill D J. Decentralized robust disturbance attenuation for a class of large-scale nonlinear systems. Syst Control Lett, 1999, 37: 71-85 CrossRef Google Scholar

[6] Jain S, Khorrami F. Decentralized adaptive output feedback design for large-scale nonlinear systems. IEEE Trans Automat Contr, 1997, 42: 729-735 CrossRef Google Scholar

[7] Zhong-Ping Jiang . Decentralized and adaptive nonlinear tracking of large-scale systems via output feedback. IEEE Trans Automat Contr, 2000, 45: 2122-2128 CrossRef Google Scholar

[8] Jiang Z P, Repperger D W. New results in decentralized adaptive non-linear stabilization using output feedback. Int J Control, 2001, 74: 659-673 CrossRef Google Scholar

[9] Yusheng Liu , Xing-Yuan Li . Decentralized robust adaptive control of nonlinear systems with unmodeled dynamics. IEEE Trans Automat Contr, 2002, 47: 848-856 CrossRef Google Scholar

[10] Shi L, Singh S K. Decentralized control for interconnected uncertain systems: extensions to higher-order uncertainties. Int J Control, 1993, 57: 1453-1468 CrossRef Google Scholar

[11] Wen C, Soh Y C. Decentralized adaptive control using integrator backstepping. Automatica, 1997, 33: 1719-1724 CrossRef Google Scholar

[12] Shoulie Xie , Lihua Xie . Decentralized stabilization of a class of interconnected stochastic nonlinear systems. IEEE Trans Automat Contr, 2000, 45: 132-137 CrossRef Google Scholar

[13] Liu S J, Zhang J F, Jiang Z P. Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems. Automatica, 2007, 43: 238-251 CrossRef Google Scholar

[14] Zhou J, Wen C. Decentralized backstepping adaptive output tracking of interconnected nonlinear systems. IEEE Trans Automat Contr, 2008, 53: 2378-2384 CrossRef Google Scholar

[15] Pan Z, Basar T. Backstepping Controller Design for Nonlinear Stochastic Systems Under a Risk-Sensitive Cost Criterion. SIAM J Control Optim, 1999, 37: 957-995 CrossRef Google Scholar

[16] Wang Q, Wei C. Decentralized robust adaptive output feedback control of stochastic nonlinear interconnected systems with dynamic interactions. Automatica, 2015, 54: 124-134 CrossRef Google Scholar

[17] Wu S, Deng F Q. Decentralized state feedback adaptive tracking for a class of stochastic nonlinear large-scale systems. In: Proceedings of the 7th International Conference on Machine Learning and Cybernetics, Kunming, 2008. 2287--2292. Google Scholar

[18] Fan H J, Xie W X. Decentralized adaptive tracking of stochastic nonlinear interconnected systems by output feedback. In: Proceedings of the 5th IEEE Conference on Industrial Electronics and Applications, Taichung, 2010. 137--142. Google Scholar

[19] Fan H, Han L, Wen C. Decentralized adaptive output-feedback controller design for stochastic nonlinear interconnected systems. Automatica, 2012, 48: 2866-2873 CrossRef Google Scholar

[20] Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive Control Design. New York: Wiley, 1995. Google Scholar

[21] Khasminskii R. Stochastic Stability of Differential Equations. Berlin: Springer, 2012. Google Scholar

[22] Hua Deng , Krstic M, Williams R J. Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. IEEE Trans Automat Contr, 2001, 46: 1237-1253 CrossRef Google Scholar

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