ZHU Saijun, LU Dunke, LI Xiaohang. Observer-based Finite-time Fault-tolerant Control for Markovian Jump Systems[J]. INFORMATION AND CONTROL, 2020, 49(2): 210-218. DOI: 10.13976/j.cnki.xk.2020.9271
Citation: ZHU Saijun, LU Dunke, LI Xiaohang. Observer-based Finite-time Fault-tolerant Control for Markovian Jump Systems[J]. INFORMATION AND CONTROL, 2020, 49(2): 210-218. DOI: 10.13976/j.cnki.xk.2020.9271

Observer-based Finite-time Fault-tolerant Control for Markovian Jump Systems

More Information
  • Received Date: May 12, 2019
  • Revised Date: December 20, 2019
  • Accepted Date: September 19, 2019
  • Available Online: December 01, 2022
  • Published Date: April 19, 2020
  • This study focuses on the finite-time fault estimation observer and fault-tolerant controller design for one-sided Lipschitz Markovian jump systems including generally uncertain transition rates. First, we propose an adaptive finite-time fault estimation observer, which is robust to unknown input, that can simultaneously estimate the states and actuator and sensor faults and ensure that the error dynamics is H finite-time-bounded. Then, on the basis of the estimated states and actuator fault, a finite-time fault-tolerant control strategy is designed to guarantee the H finite-time-boundedness of the closed-loop system. Sufficient conditions for the existence of the designed finite-time observer and controller are obtained in terms of linear matrix inequalities. Finally, a practical example is given to show the validation of the proposed method.

  • [1]
    Song X N, Wang M, Song S A, et al. Quantized output feedback control for nonlinear Markovian jump distributed parameter systems with unreliable communication links[J]. Applied Mathematics and Computation, 2019, 353(15):371-395. http://cn.bing.com/academic/profile?id=a6021463aa9fc8ee7931ddc7fec42e47&encoded=0&v=paper_preview&mkt=zh-cn
    [2]
    Shen L J, Buscher U. Solving the serial batching problem in job shop manufacturing systems[J]. European Journal of Operational Research, 2012, 221(1):14-26. doi: 10.1016/j.ejor.2012.03.001
    [3]
    Willsky A S. A survey of design methods for failure detection in dynamic systems[J]. Automatica, 1976, 12(5):601-611. http://cn.bing.com/academic/profile?id=a10e05ebb6ebc39362ef0d1dc8f4ebb5&encoded=0&v=paper_preview&mkt=zh-cn
    [4]
    Li H Y, Shi P, Yao D Y, et al. Observer-based adaptive sliding mode control for nonlinear Markovian jump systems[J]. Automatica, 2016, 64:133-142. doi: 10.1016/j.automatica.2015.11.007
    [5]
    Yin S, Yang H Y, Kaynak O. Sliding mode observer-based FTC for Markovian jump systems with actuator and sensor faults[J]. IEEE Transactions On Automatic Control, 2017, 62(7):3551-3558. doi: 10.1109/TAC.2017.2669189
    [6]
    Li X H, Karimi H R, Wang Y Y, et al. Robust fault estimation and fault-tolerant control for Markovian jump systems with general uncertain transition rates[J]. Journal of the Franklin Institute, 2018, 355(8):3508-3540. doi: 10.1016/j.jfranklin.2018.01.049
    [7]
    Lu D K, Li X H, Liu J, et al. Fault estimation and fault-tolerant control of Markovian jump system with mixed mode-dependent time-varying delays via the adaptive observer approach[J]. Journal of Dynamic Systems, Measurement and Control, 2017, 139(3):1-9. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=54e692b5782752409b9bb0d1268f2001
    [8]
    Xu Y, Lu R Q, Shi P, et al. Robust estimation for neural networks with randomly occurring distributed delays and Markovian jump coupling[J]. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(4):845-855. doi: 10.1109/TNNLS.2016.2636325
    [9]
    Shen H, Huo S C, Cao J D, et al. Generalized state estimation for Markovian coupled networks under round-robin protocol and redundant channels[J]. IEEE Transactions on Cybernetics, 2019, 49(4):1292-1301. doi: 10.1109/TCYB.2018.2799929
    [10]
    Kao H G, Xie J, Wang C H, et al. A sliding mode approach to H non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems[J]. Automatica, 2015, 52:218-226. doi: 10.1016/j.automatica.2014.10.095
    [11]
    Zhang D, Cheng J, Park J H, et al. Robust H control for nonhomogeneous Markovian jump systems subject to quantized feedback and probabilistic measurements[J]. Journal of the Franklin Institute, 2018, 355(15):6992-7010. doi: 10.1016/j.jfranklin.2018.07.011
    [12]
    周超洁, 栾小丽, 刘飞.连续时间马尔可夫跳变系统多频段多指标控制[J].信息与控制, 2018, 47(4):499-504. http://ic.sia.cn/CN/abstract/abstract12670.shtml

    Zhou C J, Luan X L, Liu F. Multi-frequency and multi-performance control for continuous-time Markov jump systems[J]. Information and Control, 2018, 47(4):499-504. http://ic.sia.cn/CN/abstract/abstract12670.shtml
    [13]
    Cheng J, Zhu H, Zhong S M, et al. Finite-time H control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals[J]. ISA Transactions, 2013, 52(6):768-774. doi: 10.1016/j.isatra.2013.07.015
    [14]
    She M Q, Yan S, Zhang G M, et al. Finite-time H static output control of Markov jump systems with an auxiliary approach[J]. Applied Mathematics and Computation, 2016, 273:553-561. doi: 10.1016/j.amc.2015.10.038
    [15]
    He S P, Liu F. Observer-based finite-time control of time-delayed jump systems[J]. Applied Mathematics and Computation, 2010, 217(6):2327-2338. doi: 10.1016/j.amc.2010.07.031
    [16]
    Zhang Y Q, Liu C X, Mu X W. Robust finite-time stabilization of uncertain singular Markovian jump systems[J]. Applied Mathematical Modelling, 2012, 36(10):5109-5121. doi: 10.1016/j.apm.2011.12.052
    [17]
    Xiong J L, Lam J, Gao H J, et al. On robust stabilization of Markovian jump systems with uncertain switching probabilities[J]. Automatica, 2005, 41(5):897-903. doi: 10.1016/j.automatica.2004.12.001
    [18]
    Yao D Y, Lu R Q, Ren H R, et al. Sliding mode control for state-delayed Markov jump systems with partly unknown transition probabilities[J]. Nonlinear Dynamics, 2018, 91(1):475-486. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=381866654154db4c0f631eaa41b6aa0a
    [19]
    Zong G D, Yang D, Hou L L, et al. Robust finite-time H control for Markovian jump systems with partially known transition probabilities[J]. Journal of the Franklin Institute, 2013, 350(6):1562-1578. doi: 10.1016/j.jfranklin.2013.04.003
    [20]
    Guo Y F, Wang Z J. Stability of Markovian jump systems with generally uncertain transition rates[J]. Journal of the Franklin Institute, 2013, 350(9):2826-2836. doi: 10.1016/j.jfranklin.2013.06.013
    [21]
    王萌, 孙雷, 尹伟, 等.一种面向交互应用的串联弹性驱动器有限时间输出反馈控制方法[J].机器人, 2016, 38(5):513-521. http://d.old.wanfangdata.com.cn/Periodical/jqr201605001

    Wang M, Sun L, Yin W, et al. A finite time output feedback control approach for interaction-oriented series elastic actuators[J]. Robot, 2016, 38(5):513-521. http://d.old.wanfangdata.com.cn/Periodical/jqr201605001
    [22]
    周映江, 蒋国平, 周帆, 等.基于滑膜方法的分布式多无人机编队控制[J].信息与控制, 2018, 47(3):306-313. doi: 10.13976/j.cnki.xk.2018.8009

    Zhou Y J, Jiang G P, Zhou F, et al. Distributed Multi-UAV formation control based on sliding mode method[J]. Information and Control, 2018, 47(3):306-313. doi: 10.13976/j.cnki.xk.2018.8009
    [23]
    刘义.马尔可夫跳变系统的有限时间稳定与镇定[D].天津: 天津大学, 2011. http://cdmd.cnki.com.cn/Article/CDMD-10056-1012023449.htm

    Liu Y. Finite-time stability and stabilization of Markov jump systems[D]. Tianjing: Tianjin University, 2011. http://cdmd.cnki.com.cn/Article/CDMD-10056-1012023449.htm
    [24]
    Kamenkov G. On stability of motion over a finite interval of time[J]. Journal of Applied Mathematics and Mechanics, 1953, 17:529-540. http://www.researchgate.net/publication/284331382_On_stability_of_motion_over_a_finite_interval_of_time
    [25]
    Zhang Y Q, Shi P, Nguang S K, et al. Observer-based finite-time fuzzy H control for discrete-time systems with stochastic jumps and time-delays[J]. Signal Processing, 2014, 97:252-261. doi: 10.1016/j.sigpro.2013.11.006
    [26]
    Yan Z G, Song Y S, Liu X P. Finite-time stability and stabilization for Itȏ-type stochastic Markovian jump systems with generally uncertain transition[J]. Applied Mathematics and Computation, 2018, 321:512-525. doi: 10.1016/j.amc.2017.10.049
    [27]
    Cao Z R, Niu Y G, Zhao H J. Finite-time sliding mode control of Markovian jump systems subject to actuator faults[J]. International Journal of Control, Automation and Systems, 2018, 16(5):2282-2289. doi: 10.1007/s12555-017-0501-8
    [28]
    Liu Y F, Ma Y C, Wang Y N. Reliable sliding mode finite-time control for discrete-time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities[J]. International Journal of Robust Nonlinear Control, 2018, 28(2):381-402. doi: 10.1002/rnc.3872
    [29]
    Li H Y, Gao H J, Shi P, et al. Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach[J]. Automatica, 2014, 50(7):1825-1834. doi: 10.1016/j.automatica.2014.04.006
    [30]
    Zhang W, Su H S, Zhu F L, et al. Unknown input observer design for one-sided Lipschitz nonlinear systems[J]. Nonlinear Dynamics, 2015, 79(2):1469-1479. doi: 10.1007/s11071-014-1754-x
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