Journal of Guangdong University of Technology ›› 2022, Vol. 39 ›› Issue (05): 46-51,60.doi: 10.12052/gdutxb.220045

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Asynchronous Control of Mode-constrained Linear Jump Systems with Time-varying Emission Probability

Zhang Lin-chuang, Du Xin-ye, Jin Hong-hong, Zhou Wei, Sun Yong-hui   

  1. College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China
  • Received:2022-03-14 Published:2022-07-18

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Abstract: The asynchronous control problem based on time-varying emission probability approach is studied for a class of mode-constrained linear jump systems. Firstly, considering the parameter and structure change of the actual system affected by external environmental factor, the semi-Markov jump system model is introduced to characterize the state change of this class of systems. Considering the mode constraints of the system, the hidden semi-Markov transition rates model and time-varying emission probability model are used to describe the mode changes of the system and the mode relationship between the system and the controller, respectively. Furthermore, an asynchronous static output feedback controller is constructed to ensure the stable operation of the system. In addition, based on Lyapunov stability theory and linear matrix inequality method, the stochastic stability conditions and the existence conditions of the controller for the closed-loop linear jump system are given. Compared with the traditional asynchronous control method based on time-invariant emission probability, the proposed asynchronous static output feedback control strategy can greatly reduce the conservatism. Finally, a numerical example is given to verify the effectiveness and correctness of the proposed asynchronous static output feedback controller.

Key words: mode-constrainted linear jump systems, semi-Markov jump system model, asynchronous output feedback control, time-varying emission probability approach

CLC Number: 

  • TG156
[1] 刘越, 周平. 马尔可夫跳变线性系统最优控制的研究现状与进展[J]. 信息与控制, 2022, 51(1): 54-68.
LIU Y, ZHOU P. Recent status and progress in optimal control of Markov jump linear systems [J]. Information and Control, 2022, 51(1): 54-68.
[2] 万海英, 栾小丽, 刘飞. 基于去随机化方法的Markov跳变系统有限频段控制[J]. 控制理论与应用, 2018, 35(7): 1002-1008.
WAN H Y, LUAN X L, LIU F. Derandomization based finite-frequency control for Markov jump system [J]. Control Theory & Applications, 2018, 35(7): 1002-1008.
[3] LI H Y, SHI P, YAO D Y. Adaptive sliding-mode control of Markov jump nonlinear systems with actuator faults [J]. IEEE Transactions on Automatic Control, 2016, 62(4): 1933-1939.
[4] TAO J, LU R Q, WU Z G, et al. Reliable control against sensor failures for Markov jump systems with unideal measurements [J]. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2017, 49(2): 308-316.
[5] HUANG J, SHI Y. Stochastic stability and robust stabilization of semi-Markov jump linear systems [J]. International Journal of Robust and Nonlinear Control, 2013, 23(18): 2028-2043.
[6] 林文娟, 何勇. 时滞半Markov跳变神经网络系统事件驱动故障检测滤波器设计[J]. 控制理论与应用, 2021, 38(9): 1341-1350.
LIN W J, HE Y. Event-triggered fault detection filter design for semi-Markov jump neural networks with time delays [J]. Control Theory & Applications, 2021, 38(9): 1341-1350.
[7] WANG B, ZHU Q X. Stability analysis of semi-Markov switched stochastic systems [J]. Automatica, 2018, 94: 72-80.
[8] SHEN H, LI F, XU S Y, et al. Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations [J]. IEEE Transactions on Automatic Control, 2017, 63(8): 2709-2714.
[9] TIAN Y X, YAN H C, ZHANG H, et al. Dynamic output-feedback control of linear semi-Markov jump systems with incomplete semi-Markov kernel [J]. Automatica, 2020, 117: 108997.
[10] ZHANG L C, LAM H K, SUN Y H, et al. Fault detection for fuzzy semi-Markov jump systems based on interval type-2 fuzzy approach [J]. IEEE Transactions on Fuzzy Systems, 2019, 28(10): 2375-2388.
[11] XU Z W, WU Z G, SU H Y, et al. Energy-to-peak filtering of semi-Markov jump systems with mismatched modes [J]. IEEE Transactions on Automatic Control, 2019, 65(10): 4356-4361.
[12] 任乘乘, 宋军, 何舒平. 基于扩展状态观测器的随机隐Markov正跳变系统有限时间异步控制[J]. 控制理论与应用, 2021, 38(11): 1891-1900.
REN C C, SONG J, HE S P. Extended-state-observer-based finite-time asynchronous control of a class of stochastic positive hidden Markov jump systems [J]. Control Theory & Applications, 2021, 38(11): 1891-1900.
[13] SONG J, NIU Y G, LAM H K, et al. Asynchronous sliding mode control of singularly perturbed semi-Markovian jump systems: application to an operational amplifier circuit [J]. Automatica, 2020, 118: 109026.
[14] XU Y, WU Z G, SUN J. Security-based passivity analysis of Markov jump systems via asynchronous triggering control[EB/OL]. (2021-07-08)[2022-03-14]. IEEE Transactions on Cybernetics, 2021. https://ieeexplore.ieee.org/document/9478308.
[15] DONG S L, WU Z G, PAN Y J, et al. Hidden-Markov-model-based asynchronous filter design of nonlinear Markov jump systems in continuous-time domain [J]. IEEE Transactions on Cybernetics, 2018, 49(6): 2294-2304.
[16] YIN Y Y, ZHU L J, LIU F, et al. Asynchronous H∞ control for nonhomogeneous higher-level Markov jump systems [J]. Journal of the Franklin Institute, 2020, 357(8): 4697-4708.
[17] CHENG P, CHEN M Y, STOJANOVIC V, et al. Asynchronous fault detection filtering for piecewise homogenous Markov jump linear systems via a dual hidden Markov model [J]. Mechanical Systems and Signal Processing, 2021, 151: 107353.
[18] TIAN Y X, YAN H C, DAI W, et al. Observed-based asynchronous control of linear semi-Markov jump systems with time-varying mode emission probabilities [J]. IEEE Transactions on Circuits and Systems II:Express Briefs, 2020, 67(12): 3147-3151.
[19] DONG S, REN W, WU Z G, et al. $ {H_\infty } $ output consensus for Markov jump multiagent systems with uncertainties [J]. IEEE Transactions on Cybernetics, 2018, 50(5): 2264-2273.
[20] ZHANG L C, SUN Y H, LI H Y, et al. Event-triggered fault detection for nonlinear semi-Markov jump systems based on double asynchronous filtering approach [J]. Automatica, 2022, 138: 110144.
[21] DONG S L, FANG M, CHEN S. Extended dissipativity asynchronous static output feedback control of Markov jump systems [J]. Information Sciences, 2020, 514: 275-287.
[22] LI M, CHEN Y, XU L Y, et al. Asynchronous control strategy for semi-Markov switched system and its application [J]. Information Sciences, 2020, 532: 125-138.
[23] 周琪, 林国怀, 马慧, 等. 输入死区下的多输入多输出系统自适应神经网络容错控制[J]. 中国科学:信息科学, 2021, 51(4): 618-632.
ZHOU Q, LIN G H, MA H, et al. Adaptive neural network fault-tolerant control for MIMO systems with dead zone inputs [J]. Scientia Sinica Informationis, 2021, 51(4): 618-632.
[24] 周琪, 陈广登, 鲁仁全, 等. 基于干扰观测器的输入饱和多智能体系统事件触发控制[J]. 中国科学:信息科学, 2019, 49(11): 1502-1516.
ZHOU Q, CHEN G D, LU R Q, et al. Disturbance-observer-based event-triggered control for multi-agent systems with input saturation [J]. Scientia Sinica Informationis, 2019, 49(11): 1502-1516.
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