具有随机逆动态的马尔可夫切换随机低阶非线性系统的有限时间镇定
Finite-Time Stabilization of Markovian Switched Stochastic Low-Order Nonlinear Systems with Stochastic Inverse Dynamics
摘要: 本文研究了一类具有马尔可夫切换和随机逆动态的随机低阶非线性系统的有限时间镇定问题。我们首先在弱解的框架下给出了有限时间稳定性理论，然后结合李雅普诺夫函数和加幂积分器技术构造了状态反馈控制器。证明了具有马尔可夫开关的随机低阶非线性系统的平凡弱解是全局有限时间稳定的。最后，通过仿真实例验证了所提设计方法的有效性。
Abstract: In this paper, we investigate the finite-time stabilization of a class of stochastic low-order nonlinear systems with Markovian switching and stochastic inverse dynamics. We first present the finite-time stability theory under the framework of weak solutions. Then, combining the Lyapunov function and adding a power integrator technique, a state feedback controller is designed to guarantee glob-al finite-time stability in probability of stochastic low-order nonlinear systems with finite-time sto-chastic inverse dynamics. Finally, the effectiveness of the proposed design method is verified by a simulation example.
文章引用：张雪, 赵桂华. 具有随机逆动态的马尔可夫切换随机低阶非线性系统的有限时间镇定[J]. 应用数学进展, 2023, 12(4): 1487-1495. https://doi.org/10.12677/AAM.2023.124154

参考文献

[1] Li, W., Wang, H. and Liu, X. (2013) State-Feedback Stabilization for Stochastic High-Order Nonlinear Systems with Markovian Switching. Journal of Mathematical Analysis and Applications, 408, 374-383. [Google Scholar] [CrossRef] 
[2] Mao, X. and Yuan, C. (2016) Stochastic Difffferential Equations with Markovian Switching. Imperial College Press, London.
[3] Wu, Z., Xie, X., Shi, P. and Xia, Y. (2009) Backstep-ping Controller Design for a Class of Stochastic Nonlinear Systems with Markovian Switching. Automatica, 45, 997-1004. [Google Scholar] [CrossRef] 
[4] Du, H., Li, S. and Qian, C. (2011) Finite-Time Attitude Tracking Control of Spacecraft with Application to Attitude Synchronization. IEEE Transactions on Automatic Control, 56, 2711-2717. [Google Scholar] [CrossRef] 
[5] Bhat, S.P. and Bernstein, D.S. (2000) Finite-Time Stability of Continuous Autonomoussystems. SIAM Journal on Control and Optimization, 38, 751-766. [Google Scholar] [CrossRef] 
[6] Yin, J., Khoo, S., Man, Z. and Yu, X. (2011) Finite-Time Sta-bility and Instability of Stochastic Nonlinear Systems. Automatica, 47, 2671-2677. [Google Scholar] [CrossRef] 
[7] Khoo, S., Yin, J., Man, Z. and Yu, X. (2013) Finite-Time Stabilization of Stochasticnonlinear Systems in Strict-Feedback Form. Automatica, 49, 1403-1410. [Google Scholar] [CrossRef] 
[8] Ai, W., Zhai, J. and Fei, S. (2013) Global Finite-Time Stabi-lization for a Class of Stochasticnonlinear Systems by Dynamic State Feedback. Kybernetika, 49, 590-600.
[9] Zhai, J. (2014) Finite-Time Output Feedback Stabilization for Stochastic High-Ordernonlinear Systems. Circuits, Systems, and Signal Processing, 33, 3809-3837. [Google Scholar] [CrossRef] 
[10] Lan, Q., Li, S., Khoo, S. and Shi, P. (2015) Global Finite-Time Stabilisation for a Class of Stochastic Nonlinear Systems by Output Feedback. Inter-national Journal of Control, 88, 494-506. [Google Scholar] [CrossRef] 
[11] Zhao, P., Feng, W., Zhao, Y. and Kang, Y. (2015) Fi-nite-Time Stochastic Input-to-Statestability of Switched Stochastic Nonlinear Systems. Applied Mathematics and Com-putation, 268, 1038-1054. [Google Scholar] [CrossRef] 
[12] Mao, X. (1999) Stability of Stochastic Differential Equations with Markovian Switching. Stochastic Processes and Their Applications, 79, 45-67. [Google Scholar] [CrossRef] 
[13] Zhao, G. and Liu, S. (2022) Finite-Time Stabilization of Non-Local Lipschitzian Stochastic Time-Varying Nonlinear Systems with Markovian Switching. Science China Infor-mation Sciences, 65, Article No. 212204. [Google Scholar] [CrossRef] 
[14] Ratnavelu, K., Kalpana, M. and Balasubramaniam, P. (2016) As-ymptotic Stability of Markovian Switching Genetic Regulatory Networks with Leakage and Mode-Dependent Time De-lays. Journal of the Franklin Institute, 353, 1615-1638. [Google Scholar] [CrossRef] 
[15] Zhu, Q. (2014) pth Moment Exponential Stability of Impulsive Stochastic Functional Differential Equations with Markovia Switching. Journal of the Franklin Institute, 351, 3965-3986. [Google Scholar] [CrossRef] 
[16] Tang, C. and Basar, T. (2001) Stochastic Stability of Singularly Perturbed Nonlinear Systems. Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, 4-7 De-cember 2001, 399-404.
[17] Tsinias, J. (1988) Stochastic Input-To-State Stability and Applications to Global Feedback Stabilization. International Journal of Control, 71, 907-930. [Google Scholar] [CrossRef] 
[18] Zhao, G.H., Li, J.C. and Liu, S.J. (2018) Finite-Time Stabilization of Weak Solutions for a Class of Non-Local Lipschitzia Stochastic Nonlinear Systems with Inverse Dynamics. Automatica, 98, 285-295. [Google Scholar] [CrossRef] 
[19] Jiang, M. and Xie, X. (2018) Finite-Time Stabilization of Stochastic Low-Order Nonlinear Systems with FT-SISS Inverse Dynamics. International Journal of Robust and Non-linear Control, 28, 1960-1972. [Google Scholar] [CrossRef] 
[20] Huang, X., Lin, W. and Yang, B. (2005) Global Finite-Time Stabilization of a Class of Uncertain Nonlinear Systems. Automatica, 41, 881-888. [Google Scholar] [CrossRef] 
[21] Mao, X., Shen, Y. and Yuan, C. (2008) Almost Surely As-ymptotic Stability of Neutral Stochastic Differential Delay Equations with Markovian Switching. Stochastic Processes and Their Applications, 118, 1385-1406. [Google Scholar] [CrossRef] 
[22] Qian, C. and Li, J. (2005) Global Finite-Time Stabilization by Out-put Feedback for Planar Systems without Observable Linearization. IEEE Transactions on Automatic Control, 50, 885-890. [Google Scholar] [CrossRef] 
[23] Liu, S., Zhang, J. and Jiang, Z. (2008) A Notion of Sto-chastic Input-to-State Stability and Its Application to Stability of Cascaded Stochastic Nonlinear Systems. Acta Mathe-maticae Applicatae Sinica, English Series, 24, 141-156. [Google Scholar] [CrossRef] 
[24] Khalil, H.K. (2002) Nonlinear Systems. 3rd Edition, Patience Hall, Hoboken, 115.

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