Event-triggered sliding mode control of networked control systems with Markovian jump parameters. (English) Zbl 1461.93318
Summary: This paper deals with sliding mode control for networked Markovian jump systems with partially-known transition probabilities via an event-triggered scheme to reduce network bandwidth usage and save network resources. First, based on the analysis of event-triggered scheme and sliding mode control, a corresponding time-delay system model is constructed by investigating the effect of the network transmission delay. Then, the less-conservative mean-square asymptotic stability of the overall closed-loop system is established. Sufficient conditions are obtained to co-design both the switching function and trigger parameters. Simultaneously, a novel control scheme is used to handle the Markovian jump parameters. Cases of completely known or unknown probabilities transition probabilities are also presented. Furthermore, the reachability of the sliding surface under the event-triggered sliding mode controller is analyzed using the Lyapunov stability theory. Finally, simulation results are provided to verify the effectiveness of the proposed design schemes.
MSC:
| 93C65 | Discrete event control/observation systems |
| 93B12 | Variable structure systems |
| 93B70 | Networked control |
| 93E03 | Stochastic systems in control theory (general) |
References:
| [1] | Basin, M. V.; Rodrłguez-Ramłrez, P. C., Sliding mode controller design for stochastic polynomial systems with unmeasured states, IEEE Transactions on Industrial Electronics, 61, 1, 387-396 (2014) |
| [2] | Basin, M. V.; Yu, P.; Shtessel, Y. B., Hypersonic missile adaptive sliding mode control using finite and fixed-time observers, IEEE Transactions on Industrial Electronics, 65, 1, 930-941 (2018) |
| [3] | Bolzern, P.; Colaneri, P.; Nicolao, G. D., Markov jump linear systems with switching transition rates: Mean square stability with dwell-time, Automatica, 46, 1081-1088 (2010) · Zbl 1192.93119 |
| [4] | Cao, Z.; Niu, Y.; Lam, H. K.; Zhao, J., Sliding mode control of Markovian jump fuzzy systems: A dynamic event-triggered method, IEEE Transactions on Fuzzy Systems (2020) |
| [5] | Cao, Z.; Niu, Y.; Song, J., Finite-time sliding mode control of Markovian jump cyber-physical systems against randomly occurring injection attacks, IEEE Transactions on Automatic Control (2019) · Zbl 1533.93672 |
| [6] | Chadli, M.; Darouach, M., Further enhancement on robust \(H_\infty\) control design for discrete-time singular systems, IEEE Transactions on Automatic Control, 59, 2, 494-499 (2014) · Zbl 1360.93382 |
| [7] | Dong, S.; Philip, Chen C. L.; Fang, M.; Wu, Z., Dissipativity-based asynchronous fuzzy sliding mode control for T-S fuzzy hidden Markov jump systems, IEEE Transactions on Cybernetics, 50, 9, 4020-4030 (2019) |
| [8] | Fang, M.; Shi, P.; Dong, S., Sliding mode control for Markov jump systems with delays via asynchronous approach, IEEE Transactions on Systems, Man, and Cybernetics: Systems (2019) |
| [9] | Feng, X.; Loparo, K. A.; Ji, Y.; Chizeck, H. J., Stochastic stability properties of jump linear systems, IEEE Transactions on Automation Control, 37, 1, 38-53 (1992) · Zbl 0747.93079 |
| [10] | Heemels, W.; Donkers, M., Model-based periodic event-triggered control for linear systems, Automatica, 49, 3, 698-711 (2013) · Zbl 1267.93102 |
| [11] | Huang, J.; Cai, F.; Huang, J.; Wang, W., \( L_2- L_\infty\) FIltering for networked switched systems with multiple packet dropouts via random switched Lyapunov function, International Journal of Innovative Computing, Information and Control, 16, 1, 123-135 (2020) |
| [12] | Ji, Y.; Chizeck, H. J., Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control, IEEE Transactions on Automatic Control, 35, 7, 777-788 (1990) · Zbl 0714.93060 |
| [13] | Li, F.; Du, C.; Yang, C.; Wu, L.; Gui, W., Finite-time asynchronous sliding mode control for Markovian jump systems, Automatica (2019) · Zbl 1429.93050 |
| [14] | Li, H.; Gao, H.; Shi, P.; Zhao, X., Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach, Automatica, 50, 7, 1825-1834 (2014) · Zbl 1296.93200 |
| [15] | Li, L.; Shi, P.; Agarwal, R. K.; Ahn, C. K.; Xing, W., Event-triggered model predictive control for multiagent systems with communication constraints, IEEE Transactions on Systems, Man, and Cybernetics: Systems (2019) |
| [16] | Li, H.; Shi, P.; Yao, D.; Wu, L., Observer-based adaptive sliding mode control for nonlinear Markovian jump systems, Automatica, 64, 133-142 (2016) · Zbl 1329.93126 |
| [17] | Li, H.; Wang, Y.; Yao, D.; Lu, R., A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems, Automatica, 97, 404-413 (2018) · Zbl 1406.93370 |
| [18] | Liu, X.; Su, X.; Shi, P.; Shen, C.; Peng, Y., Event-triggered sliding mode control of nonlinear dynamic systems, Automatica (2020) · Zbl 1430.93029 |
| [19] | Liu, J.; Yin, Y.; Luo, W.; Vazquez, S.; Wu, L., Sliding mode control of a three-phase AC/DC voltage source converter under unknown load conditions: Industry Applications, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48, 99, 1771-1780 (2017) |
| [20] | Ma, H.; Li, H.; Lu, R.; Huang, T., Adaptive event-triggered control for a class of nonlinear systems with periodic disturbances, SCIENCE CHINA Information Sciences, 63, 5, 161-175 (2020) |
| [21] | Mahmoud, R. J.; Alireza, S., Stabilization of networked control systems with sparse observer-controller networks, IEEE Transactions on Automatic Control, 60, 6, 1686-1691 (2015) · Zbl 1360.93611 |
| [22] | Ning, Z.; Zhang, L.; Colaneri, P., Semi-Markov jump linear systems with incomplete sojourn and transition information: Analysis and synthesis, IEEE Transactions on Automatic Control, 65, 1, 159-174 (2020) · Zbl 1483.93689 |
| [23] | Niu, Y.; Ho, D. W.C., Design of sliding mode control subject to packet losses, IEEE Transactions on Automatic Control, 55, 11, 2623-2628 (2010) · Zbl 1368.93087 |
| [24] | Pisanoa, A.; Tanellib, M.; Ferrarac, A., Switched/time-based adaptation for second-order sliding mode control, Automatica, 64, 126-132 (2016) · Zbl 1329.93044 |
| [25] | Ren, H.; Zong, G.; Li, T., Event-triggered finite-time control for networked switched linear systems with asynchronous switching, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48, 11, 1874-1884 (2018) |
| [26] | Shen, Y.; Wu, Z.; Shi, P.; Wen, G., Dissipativity based fault detection for 2D Markov jump systems with asynchronous modes, Automatica, 106, 8-17 (2019) · Zbl 1429.93388 |
| [27] | Song, H.; Chen, S.; Yam, Y., Sliding mode control for discrete-time systems with Markovian packet dropouts, IEEE Transactions on Cybernetics, 47, 11, 3669-3679 (2017) |
| [28] | Song, J.; Niu, Y.; Xu, J., An event-triggered approach to sliding mode control of Markovian jump lur’e systems under hidden mode detections, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50, 4, 1514-1525 (2020) |
| [29] | Song, J.; Niu, Y.; Zou, Y., Finite-time stabilization via sliding mode control, IEEE Transactions on Automatic Control, 62, 3, 1478-1483 (2017) · Zbl 1366.93106 |
| [30] | Su, X.; Liu, X.; Shi, P.; Song, Y., Sliding mode control of hybrid switched systems via an event-triggered mechanism, Automatica, 90, 294-303 (2018) · Zbl 1387.93055 |
| [31] | Sun, H.; Li, Y.; Zong, G.; Hou, L., Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities, Automatica, 89, 349-357 (2018) · Zbl 1388.93100 |
| [32] | Wang, B.; Meng, X.; Chen, T., Event based pulse-modulated control of linear stochastic systems, IEEE Transactions on Automatic Control, 59, 8, 2144-2150 (2014) · Zbl 1360.93658 |
| [33] | Wibisono, W.; Ahmad, T.; Ijtihadie, R. M.; Pertiwi, K. M.D., A node density-based approach for energy-efficient data gathering protocol in wireless sensor network environments, International Journal of Innovative Computing, Information and Control, 16, 2, 681-700 (2020) |
| [34] | Wu, Z.; Dong, S.; Shi, P.; Su, H.; Huang, T., Reliable filtering of nonlinear Markovian jump systems: The continuous-time case, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49, 2, 386-394 (2019) |
| [35] | Wu, L.; Gao, Y.; Liu, J.; Li, H., Event-triggered sliding mode control of stochastic systems via output feedback, Automatica, 82, 79-92 (2017) · Zbl 1376.93030 |
| [36] | Wu, Z.; Su, H.; Chu, J., Delay-dependent \(H_\infty\) control for singular Markovian jump systems with time delay, Optimal Control Applications & Methods, 30, 5, 443-461 (2009) |
| [37] | Zhou, Q.; Chen, G. D.; Lu, R. Q.; Bai, W. W., Disturbance-observer-based event-triggered control for multi-agent systems with input saturation, SCIENTIA SINICA Informationis, 49, 11, 1502-1516 (2019) |
| [38] | Zhou, Q.; Wang, W.; Liang, H.; Basin, M.; Wang, B., Observer-based event-triggered fuzzy adaptive bipartite containment control of multi-agent systems with input quantization, IEEE Transactions on Fuzzy Systems (2019) |
| [39] | Zhou, Q.; Wang, W.; Ma, H.; Li, H., Event-triggered fuzzy adaptive containment control for nonlinear multi-agent systems with unknown Bouc-wen hysteresis input, IEEE Transactions on Fuzzy Systems (2019) |
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