Stochastic stabilization of Markovian jump cloud control systems based on max-plus algebra

doi:10.23919/JSEE.2022.000082

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (4): 827-834.doi: 10.23919/JSEE.2022.000082

• CLOUD CONTROL SYSTEMS • Previous Articles Next Articles

Stochastic stabilization of Markovian jump cloud control systems based on max-plus algebra

Jin WANG¹(), Hongjiu YANG^1,*(), Yuanqing XIA²(), Ce YAN²()

¹ School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
² School of Automation, Beijing Institute of Technology, Beijing 100081, China

Received:2022-03-01 Online:2022-08-30 Published:2022-08-30
Contact: Hongjiu YANG E-mail:jinwang_auto@tju.edu.cn;yanghongjiu@tju.edu.cn;xia_yuanqing@bit.edu.cn;yancemc@163.com
About author:|WANG Jin was born in 1996. He received his B.E. degree in automation from Tianjin University, Tianjin, China, in 2018. He is currently pursuing his M.S. degree in control science and engineering in the Department of Automation, School of Electrical and Information Engineering, Tianjin University, Tianjin, China. His current research interests include discrete-event systems, stochastic control and cloud control system. E-mail: jinwang_auto@tju.edu.cn||YANG Hongjiu was born in 1982. He received his B.S. degree in mathematics and applied mathematics and M.S. degree in applied mathematics from Hebei University of Science and Technology, Shijiazhuang, China, in 2005 and 2008, respectively. He received his Ph.D. degree in control science and engineering from Beijing Institute of Technology, Beijing, China. He was an associate professor with Department of Automation, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, China, in 2013. He is currently a professor with Department of Automation, School of Electrical and Information Engineering, Tianjin University, China. His main research interests include robust control/filter theory, delta operator systems, networked control systems and active disturbance rejection control. E-mail: yanghongjiu@tju.edu.cn||XIA Yuanqing was born in 1971. He received his M.S. degree in fundamental mathematics from Anhui University, China, in 1998 and Ph.D. degree in control theory and control engineering from Beijing University of Aeronautics and Astronautics, Beijing, China, in 2001. From January 2002 to November 2003, he was a postdoctoral research associate with the Institute of Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China. From November 2003 to February 2004, he was with the National University of Singapore as a research fellow, where he worked on variable structure control. From February 2004 to February 2006, he was with the University of Glamorgan, Pontypridd, U.K., as a research fellow. From February 2007 to June 2008, he was a guest professor with Innsbruck Medical University, Innsbruck, Austria. Since 2004, he has been with the School of Automation, Beijing Institute of Technology, Beijing, first as an associate professor, then, since 2008, as a professor. His current research interests include networked control systems, robust control, signal processing, and active disturbance rejection control. E-mail: xia_yuanqing@bit.edu.cn||YAN Ce was born in 1990. He received his B.S. degree in mathematics and applied mathematics from Hebei University of Science and Technology, Shijiazhuang, China, in 2014, and M.E. degree in control theory and control engineering from Yanshan University, Qinhuangdao, China, in 2017. He is currently working toward his Ph.D. degree in control science and engineering with Beijing Institute of Technology, Beijing, China. His research interests include cloud control systems and application, cloud workflow scheduling, industrial IoT, and intelligent manufacturing systems. E-mail: yancemc@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (61973230) and Tianjin Research Innovation Project for Postgraduate Students (2021YJSO2S03)

Abstract

Abstract:

In this paper, stochastic stabilization is investigated by max-plus algebra for a Markovian jump cloud control system with a reference signal. For the Markovian jump cloud control system, there exists framework adjustment whose evolution is satisfied with a Markov chain. Using max-plus algebra, a max-plus stochastic system is used to describe the Markovian jump cloud control system. A causal feedback matrix is obtained by exponential stability analysis for a causal feedback controller of the Markovian jump cloud control system. A sufficient condition is given to ensure existence on the causal feedback matrix of the causal feedback controller. Based on the causal feedback controller, stochastic stabilization in probability is analyzed for the Markovian jump cloud control system with a reference signal. Simulation results are given to show effectiveness of the causal feedback controller for the Markovian jump cloud control system.

Key words: Markovian jump cloud control system, causal feedback controller, max-plus algebra, max-product algebra, stochastic stabilization

Jin WANG, Hongjiu YANG, Yuanqing XIA, Ce YAN. Stochastic stabilization of Markovian jump cloud control systems based on max-plus algebra[J]. Journal of Systems Engineering and Electronics, 2022, 33(4): 827-834.

Figures/Tables 7

Fig 1

Fig 2

Fig 3

Fig 4

Fig 5

Fig 6

Fig 7

References 32

1	SHEN J, ZHOU T Q, HE D B, et al Block design-based key agreement for group data sharing in cloud computing. IEEE Trans. on Dependable and Secure Computing, 2019, 16 (6): 996- 1010. doi: 10.1109/TDSC.2017.2725953
2	TAN H R, WANG Y N, ZHONG H, et al Coordination of low-power nonlinear multi-agent systems using cloud computing and a data-driven hybrid predictive control method. Control Engineering Practice, 2021, 108, 104722. doi: 10.1016/j.conengprac.2020.104722
3	SHA W Y, ZHU Y X, CHEN M, et al Statistical learning for anomaly detection in cloud server systems: a multi-order Markov chain framework. IEEE Trans. on Cloud Computing, 2018, 6 (2): 401- 413. doi: 10.1109/TCC.2015.2415813
4	XIA Y Q Cloud control systems. IEEE/CAA Journal of Automatica Sinica, 2015, 2 (2): 134- 142. doi: 10.1109/JAS.2015.7081652
5	CHUA M Y K, YU F R, BU S R Dynamic operations of cloud radio access networks (C-RAN) for mobile cloud computing systems. IEEE Trans. on Vehicular Technology, 2016, 65 (3): 1536- 1548. doi: 10.1109/TVT.2015.2411739
6	ZHOU B W, DASTJERDI A V, CALHEIROS R N, et al mCloud: a context-aware offloading framework for heterogeneous mobile cloud. IEEE Trans. on Services Computing, 2017, 10 (5): 797- 810. doi: 10.1109/TSC.2015.2511002
7	LIU G P Predictive control of networked multiagent systems via cloud computing. IEEE Trans. on Cybernetics, 2017, 47 (8): 1852- 1859. doi: 10.1109/TCYB.2017.2647820
8	YANG H J, JU S, XIA Y Q, et al Predictive cloud control for networked multiagent systems with quantized signals under DoS attacks. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2021, 51 (2): 1345- 1353. doi: 10.1109/TSMC.2019.2896087
9	LUO F, JIANG C X, YU S, et al Stability of cloud-based UAV systems supporting big data acquisition and processing. IEEE Trans. on Cloud Computing, 2019, 7 (3): 866- 877. doi: 10.1109/TCC.2017.2696529
10	MAHMOUD M, HAMDAN M Fundamental issues in networked control systems. IEEE/CAA Journal of Automatica Sinica, 2018, 5 (5): 902- 922. doi: 10.1109/JAS.2018.7511162
11	MAIA C, ANDRADE C, HARDOUIN L On the control of max-plus linear system subject to state restriction. Automatica, 2011, 47 (5): 988- 992. doi: 10.1016/j.automatica.2011.01.047
12	WANG C L, TAO Y G, YANG P, et al Dimension reduction and feedback stabilization for max-plus linear systems and applications in VLSI array processors. IEEE Trans. on Automatic Control, 2017, 62 (12): 6353- 6368. doi: 10.1109/TAC.2017.2708508
13	LOPES G, KERSBERGEN B, VAN DEN BOOM T, et al Modeling and control of legged locomotion via switching max-plus models. IEEE Trans. on Robotics, 2014, 30 (3): 652- 665. doi: 10.1109/TRO.2013.2296105
14	MERLET G Cycle time of stochastic max-plus linear systems. Electronic Journal of Probability, 2008, 13 (12): 322- 340.
15	VAN DEN BOOM T, DE SCHUTTER B Modelling and control of discrete event systems using switching max-plus-linear systems. Control Engineering Practice, 2006, 14 (10): 1199- 1211. doi: 10.1016/j.conengprac.2006.02.006
16	VAN DEN BOOM T, DE SCHUTTER B Modeling and control of switching max-plus-linear systems with random and deterministic switching. Discrete Event Dynamic Systems, 2012, 22 (3): 293- 332. doi: 10.1007/s10626-011-0123-x
17	DE FARIAS D, GEROMEL J, DO VAL J, et al Output feedback control of Markov jump linear systems in continuous-time. IEEE Trans. on Automatic Control, 2000, 45 (5): 944- 949. doi: 10.1109/9.855557
18	SONG J, NIU Y G, LAM J, et al A hybrid design approach for output feedback exponential stabilization of Markovian jump systems. IEEE Trans. on Automatic Control, 2018, 63 (5): 1404- 1417. doi: 10.1109/TAC.2018.2791349
19	ZHENG C D, SHAN Q H, ZHANG H G, et al On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching. IEEE Trans. on Neural Networks and Learning Systems, 2013, 24 (5): 800- 811. doi: 10.1109/TNNLS.2013.2244613
20	YUKSEL S, MEYN S Random-time, state-dependent stochastic drift for Markov chains and application to stochastic stabilization over erasure channels. IEEE Trans. on Automatic Control, 2013, 58 (1): 47- 59. doi: 10.1109/TAC.2012.2204157
21	ZADE B, MANSOURI N, JAVIDI M SAEA: a security-aware and energy-aware task scheduling strategy by parallel squirrel search algorithm in cloud environment. Expert Systems with Applications, 2021, 176, 114915. doi: 10.1016/j.eswa.2021.114915
22	MARINESCU D Cloud computing. Waltham: Morgan Kaufmann, 2018.
23	WANG C L, TAO Y G, YANG P, et al Parallel task assignment optimization algorithm and parallel control for cloud control system. Acta Automatica Sinica, 2017, 43 (11): 1973- 1983.
24	TROBEC R, VAJTERSIC M, ZINTERHOF P. Parallel computing. Berlin: Springer-Verlag, 2009.
25	WANG J J, HU X J, HE C Reactive scheduling of multiple EOSs under cloud uncertainties: model and algorithms. Journal of Systems Engineering and Electronics, 2021, 32 (1): 163- 177. doi: 10.23919/JSEE.2021.000015
26	JIA Y F, ZHOU Z Q, WU R B A workload-based nonlinear approach for predicting available computing resources. Journal of Systems Engineering and Electronics, 2020, 31 (1): 224- 230.
27	KORDONIS I, MARAGOS P, PAPAVASSILOPOULOS G Stochastic stability in max-product and max-plus systems with Markovian jumps. Automatica, 2017, 92, 123- 132.
28	BACCELLI F, COHEN G, OLSDER G, et al. Synchronization and linearity: an algebra for discrete event systems. New York: John Wiley and Sons, 1992.
29	GAUBERT S, SERGEEV S The level set method for the two-sided eigenproblem. Discrete Event Dynamic Systems, 2012, 23 (2): 105- 134.
30	GONÇALVES V, MAIA C, HARDOUIN L On max-plus linear dynamical system theory: the regulation problem. Automatica, 2017, 75, 202- 209. doi: 10.1016/j.automatica.2016.09.019
31	CHANG C S On the exponentiality of stochastic linear systems under the max-plus algebra. IEEE Trans. on Automatic Control, 1996, 41 (8): 1182- 1188. doi: 10.1109/9.533680
32	YUAN H H, XIA Y Q, LIN M, et al Dynamic pricing-based resilient strategy design for cloud control system under jamming attack. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2020, 50 (1): 111- 122. doi: 10.1109/TSMC.2019.2952467

Stochastic stabilization of Markovian jump cloud control systems based on max-plus algebra

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 7

References 32

Related Articles 0

Recommended Articles

Metrics

Comments