Abstract
This paper addresses the problem of output feedback stabilization for stochastic nonlinear time-varying delay systems with an unknown output function. A remarkable feature of the system to be considered is the simultaneous presence of a continuous unknown sensitivity function and the stochastic disturbances, which have not been treated together before. A new observer is designed by using a dynamic gain without using the information on unknown time-varying delay and nonlinearities. With the aid of the observer, an output feedback controller is constructed by the stochastic double-domination method, where two gains are used to handle the unknown output function and nonlinearities. The performance of the system is analyzed in detail via two integral Lyapunov functions. Finally, the efficiency of the control strategy is illustrated by a simulation example.
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P. Pepe and Z. P. Jiang, “A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems,” Systems & Control Letters, vol. 55, no. 12, pp. 1006–1014, 2006.
X. F. Zhang, L. Baron, Q. R. Liu, and E. K. Boukas, “Design of stabilizing controllers with a dynamic gain for feedforward nonlinear time-delay systems,” IEEE Transactions on Automatic Control, vol. 56, no. 3, pp. 692–697, 2011.
Z. B. Song, Z. Y. Sun, S. H. Yang, and T. Li, “Global stabilization via nested saturation function for high-order feedforward nonlinear systems with unknown time-varying delays,” International Journal of Robust Nonlinear Control, vol. 26, no. 15, pp. 3363–3387, 2016.
B. Li, H. Shen, X. N. Song, and J. J. Zhao, “Robust exponential H∞ control for uncertain time-varying delay systems with input saturation: A Markov jump model approach,” Applied Mathematics and Computation, vol. 237, pp. 190–202, 2014.
S. H. Yang, Z. Y. Sun, Z. Wang, and T. Li, “A new approach to global stabilization of high-order time-delay uncertain nonlinear systems via time-varying feedback and homogeneous domination,” Journal of the Franklin Institute, vol. 355, no. 14, pp. 6469–6492, 2018.
Z. F. Li, T. S. Li, and G. Feng, “Adaptive neural control for a class of stochastic nonlinear time-delay systems with unknown dead zone using dynamic surface technique,” International Journal of Robust Nonlinear Control, vol. 26, no. 4, pp. 759–781, 2016.
Z. Y. Sun, S. H. Yang, and T. Li, “Global adaptive stabilization for high-order uncertain time-varying nonlinear systems with time-delays,” International Journal of Robust Nonlinear Control, vol. 27, no. 13, pp. 2198–2217, 2016.
Z. R. Xiang and R. H. Wang, “Robust control for uncertain switched non-linear systems with time delay under asynchronous switching,” IET Control Theory and Applications, vol. 3, no. 8, pp. 1041–1050, 2009.
Z. Y. Sun, X. H. Zhang, and X. J. Xie, “Continuous global stabilisation of high-order time-delay nonlinear systems,” International Journal of Control, vol. 86, no. 6, pp. 994–1007, 2013.
Z. R. Cao, Y. G. Niu, and H. R. Karimi, “Sliding mode control of automotive electronic valve system under weight Try-Once-Discard protocol,” Information Sciences, vol. 515, pp. 324–340, 2020.
J. Li and C. J. Qian, “Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems,” IEEE Transactions on Automatic Control, vol. 51, no. 5, pp. 879–884, 2006.
C. J. Qian and W. Lin, “Recursive observer design, homogeneous approximation, and nonsmooth output feedback stabilization of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 51, no. 9, pp. 1457–1471, 2006.
J. R. Li, Y. G. Niu, and Y. K. Yang, “Output-feedback control under hidden Markov analog fading and redundant channels,” IEEE Transactions on Circuits and Systems-II: Express Briefs, vol. 68, no. 8, pp. 2922–2926, 2021.
F. Z. Li and Y. G. Liu, “Global stabilization via timevarying output-feedback for stochastic nonlinear systems with unknown growth rate,” Systems & Control Letters, vol. 77, pp. 69–79, 2015.
Q. X. Lan, S. H. Li, S. Y. Khoo, and P. Shi, “Global finitetime stabilisation for a class of stochastic nonlinear systems by output feedback,” International Journal of Control, vol. 88, no. 3, pp. 494–506, 2015.
Y. D. Wang, J. W. Xia, Z. Wang, and H. Shen, “Design of a fault-tolerant output-feedback controller for thickness control in cold rolling mills,” Applied Mathematics and Computation, vol. 369, p. 124841, 2020.
Y. G. Liu, “Global asymptotic regulation via time-varying output feedback for a class of uncertain nonlinear systems,” SIAM Journal on Control and Optimization, vol. 51, no. 6, pp. 4318–4342, 2013.
H. Shen, M. C. Dai, H. C. Yan, and J. H. Park, “Quantized output feedback control for stochastic semi-Markov jump systems with unreliable links,” Transactions on Circuits and Systems II: Express Briefs, vol. 65, no. 12, pp. 1998–2002, 2018.
Z. Y. Sun, Y. Shao, C. C. Chen, and Q. H. Meng, “Global output-feedback stabilization for stochastic nonlinear systems: A double-domination approach,” International Journal of Robust Nonlinear Control, vol. 28, no. 15, pp. 4635–4646, 2018.
J. Wang, M. S. Chen, H. Shen, J. H. Park, and Z. G. Wu, “A Markov jump model approach to reliable eventtriggered retarded dynamic output feedback H∞ control for networked systems,” Nonlinear Analysis: Hybrid Systems, vol. 26, pp. 137–150, 2017.
Z. N. Zhang, Y. G. Niu, and B. Chen, “Static output feedback sliding mode control under rice fading channel: An interval type-2 fuzzy modelling method,” IET Control Theory and Applications, vol. 14, no. 19, pp. 3230–3239, 2021.
Z. Y. Sun, D. Zhang, C. C. Chen, and Q. H. Meng, “Feedback stabilisation of time-delay nonlinear systems with continuous time-varying output function,” International Journal of Systems Science, vol. 50, no. 2, pp. 244–255, 2018.
Z. Y. Sun, J. W. Xing, and C. C. Chen, “Output feedback stabilization of time-delay nonlinear systems with unknown continuous time-varying output function and nonlinear growth rate,” International Journal of Robust Nonlinear Control, vol. 30, no. 6, pp. 2579–2592, 2018.
W. M. He, J. Guo, and Z. R. Xiang, “Global sampleddata output feedback stabilization for a class of stochastic nonlinear systems with time-varying delay,” Journal of the Franklin Institute, vol. 356, no. 1, pp. 292–308, 2019.
J. Wang, S. C. Huo, J. W. Xia, J. H. Park, X. Huang, and H. Shen, “Generalised dissipative asynchronous output feedback control for Markov jump repeated scalar non-linear systems with time-varying delay,” IET Control Theory & Applications, vol. 13, no. 13, pp. 2114–2121, 2019.
Z. Y. Sun, J. W. Xing, and Q. H. Meng, “Output feedback regulation of time-delay nonlinear systems with unknown continuous output function and unknown growth rate,” Nonlinear Dynamics , vol. 100, no. 2, pp. 1309–1325, 2020.
Y. X. Zhao, P. Chen, and H. L. Yang, “Optimal periodic dividend and capital injection problem for spectrally positive Levy processes,” Insurance: Mathematics and Economics, vol. 74, pp. 135–146, 2017.
Z. R. Cao, Y. G. Niu, and H. R. Karimi, “Dynamic output feedback sliding mode control for Markovian jump systems under stochastic communication protocol and its application,” International Journal of Robust and Nonlinear Control, vol. 30, no. 17, pp. 7307–7325, 2020.
W. T. Zha, J. Y. Zhai, and S. M. Fei, “Output feedback control for a class of stochastic high-order nonlinear systems with time-varying delays,” International Journal of Robust Nonlinear Control, vol. 24, no. 16, pp. 2243–2260, 2013.
W. Q. Ai, J. Y. Zhai, and J. M. Fei, ”Global output feedback stabilization for a class of stochastic feedforward nonlinear systems with time-varying input delay,” Transactions of the Institute of Measurement and Control, vol. 38, no. 3, pp. 356–363, 2016.
X. J. Xie and M. M. Jiang, “Output feedback stabilization of stochastic feedforward nonlinear time-delay systems with unknown output function,” International Journal of Robust Nonlinear Control, vol. 28, no. 1, pp. 266–280, 2018.
X. R. Mao, Stochastic Differential Equations and Applications, Horwood Publishing, Chichester, UK, 1997.
D. X. Yu, C. L. P. Chen, C. E. Ren, and S. Sui, “Swarm control for self-organized system with fixed and switching topologyn,” IEEE Transactions on Cybernetics, vol. 50, no. 10, pp. 4481–4494, 2020
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Mengmeng Gao received her B.S. degree in mathematics from Liaocheng University in 2019. She is studying for an M.S. degree in Liaocheng University. Her current research interests include stochastic nonlinear systems and adaptive control.
Junsheng Zhao was born in 1981. He received his M.S. degree from Qufu Normal University in 2006, and a Ph.D. degree from Southeast University, China, in 2015. He was a Visiting Scholar with the Department of Mathematics and Statistics, University of Strathclyde, UK, in 2020. Since 2006, he has been with the School of Mathematical Science, Liaocheng University, where he is currently an associate professor. His current research interests include stochastic control, adaptive control, and stability theory of stochastic systems.
Zong-Yao Sun was born in 1979. He received his M.S. degree from Qufu Normal University in 2005, and a Ph.D. degree from Shandong University, China, in 2009. He was a Visiting Scholar with the Department of Electrical and Computer Engineering, University of Texas at San Antonio, USA, in 2016. Since 2009, he has been with the Institute of Automation, Qufu Normal University, where he is currently a professor. His current research interests include nonlinear control, adaptive control, and stability theory of time-delay systems. Prof. Sun won the title of Taishan Scholar in 2021, and was awarded the Shandong Province Outstanding Tutor of Graduate Students in 2019.
Jianwei Xia is a professor of the School of Mathematics Science, Liaocheng University. He received his Ph.D. degree in automatic control from Nanjing University of Science and Technology in 2007. From 2010 to 2012, he worked as a Postdoctoral Research Associate in the School of Automation, Southeast University, Nanjing, China. From 2013 to 2014, he worked as a Postdoctoral Research Associate in the Department of Electrical Engineering, Yeungnam University, Gyeongsan, Korea. His research topics are robust control, stochastic systems, and neural networks.
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Gao, M., Zhao, J., Sun, ZY. et al. Output Feedback Stabilization of Stochastic Nonlinear Time-varying Delay Systems with Unknown Output Function. Int. J. Control Autom. Syst. 20, 2839–2848 (2022). https://doi.org/10.1007/s12555-021-0639-2
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DOI: https://doi.org/10.1007/s12555-021-0639-2