This is an open access article published by the IET under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)
Uncertain dynamics in communication network, including random delays and packet losses make it difficult to guarantee stability of cyber-physical systems (CPSs). Many existing works consider the uncertainties of network channel with strong assumptions that network delay bounds and its distribution are known a priori and time-invariant. However, these assumptions could be invalidated in realistic CPSs by malicious attacks, system hardware faults, topology changes etc. A probability density function (PDF)-based tuning of stochastic optimal control (PTSOC) is proposed to manage the unknown dynamics in the embedded network. The update law of the proposed controller is derived and updated based on the PDF estimation of network delays that explicitly consider delays and its time-varying distribution. The results illustrate that the proposed PTSOC has a better performance in terms of the overshoot, convergence time, and cost when compared with the conventional stochastic optimal control.
References
-
-
1)
-
5. Gao, H., Chen, T.: ‘Network-based H∞ output tracking control’, IEEE Trans. Autom. Control, 2008, 53, (3), pp. 655–667 (doi: 10.1109/TAC.2008.919850).
-
2)
-
3. Ji, X., Yu, H., Fan, G., et al: ‘Attack-defense trees based cyber security analysis for CPSs’. 2016 17th IEEE/ACIS Int. Conf. on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD), Shanghai, 2016, pp. 693–698.
-
3)
-
19. Chen, X., Tharmarasa, R., Kirubarajan, T., et al: ‘Online clutter estimation using a Gaussian kernel density estimator for multitarget tracking’, IET Radar Sonar Navig. , 2015, 9, (1), pp. 1–9.
-
4)
-
7. Hao, F., Zhao, X.: ‘Linear matrix inequality approach to static output feedback stabilisation of discrete-time networked control systems’, IETControl Theory Applic., 2010, 4, (7), pp. 1211–1221 (doi: 10.1049/iet-cta.2009.0164).
-
5)
-
17. Tiberi, U., Fischione, C., Johansson, K.H., et al: ‘Energy-efficient sampling of networked control systems over IEEE 802.15.4 wireless networks’, Automatica, 2013, 49, (3), pp. 712–724 (doi: 10.1016/j.automatica.2012.11.046).
-
6)
-
6. Gao, H., Meng, X., Chen, T.: ‘Stabilization of networked control systems with a new delay characterization’, IEEE Trans. Autom. Control, 2008, 53, (9), pp. 2142–2148 (doi: 10.1109/TAC.2008.930190).
-
7)
-
18. He, Y., Mao, Y., Chen, W., et al: ‘Nonlinear metric learning with kernel density estimation’, IEEE Trans. Knowl. Data Eng., 2015, 27, (6), pp. 1602–1614 (doi: 10.1109/TKDE.2014.2384522).
-
8)
-
8. Tian, E., Yue, D., Peng, C.: ‘Brief paper: reliable control for networked control systems with probabilistic sensors and actuators faults’, Inst. Inf. Control Eng., 2010, 4, (8), pp. 1478–1488.
-
9)
-
1. Xie, S., Low, K., Gunawan, E.: ‘An adaptive tuning algorithm for IEEE 802.15.4-based network control system’. IEEE Ninth Int. Conf. on Intelligent Sensors, Sensor Networks and Information Processing, 2014, pp. 1–6.
-
10)
-
2. Lee, K., Lee, S., Lee, M.: ‘QoS-based remote control of networked control systems via profibus token passing protocol’, IEEE Trans. Ind. Inf., 2005, 1, (3), pp. 183–191 (doi: 10.1109/TII.2005.852064).
-
11)
-
16. Calabrese, R., Zenga, M.: ‘Bank loan recovery rates: measuring and nonparametric density estimation’, J. Bank. Fin., 2010, 34, (5), pp. 903–911 (doi: 10.1016/j.jbankfin.2009.10.001).
-
12)
-
13. Silverman, B.W.: ‘Density estimation for statistics and data analysis’ (CRC Press, 1986, vol. 26).
-
13)
-
21. Carnevale, D., Teel, A.R., Nesic, D.: ‘A lyapunov proof of an improved maximum allowable transfer interval for networked control systems’, IEEE Trans. Autom. Control, 2007, 52, (5), pp. 892–897 (doi: 10.1109/TAC.2007.895913).
-
14)
-
17. Elgammal, A., Duraiswami, R., Davis, L.S.: ‘Efficient kernel density estimation using the fast gauss transform with applications to color modeling and tracking’, IEEE Trans. Pattern Anal. Mach. Intell., 2003, 25, (11), pp. 1499–1504 (doi: 10.1109/TPAMI.2003.1240123).
-
15)
-
4. Mitchell, R., Chen, I.R.: ‘Modeling and analysis of attacks and counter defense mechanisms for cyber physical systems’, IEEE Trans. Reliab., 2016, 65, (1), pp. 350–358 (doi: 10.1109/TR.2015.2406860).
-
16)
-
20. Gisbert, F.: ‘Weighted samples, kernel density estimators and convergence’, Empir. Econ., 2003, 28, pp. 335–351 (doi: 10.1007/s001810200134).
-
17)
-
4. Liu, G.-P., Xia, Y., Rees, D.,, et al: ‘Design and stability criteria of networked predictive control systems with random network delay in the feedback channel’, IEEE Trans. Syst. Man Cybern. C Appl. Rev., 2007, 37, (2), pp. 173–184 (doi: 10.1109/TSMCC.2006.886987).
-
18)
-
15. Bors, A.G., Nasios, N.: ‘Kernel bandwidth estimation for nonparametric modelling’, IEEE Trans. Syst. Man Cybern. B Cybern., 2009, 39, (6), pp. 1543–1555 (doi: 10.1109/TSMCB.2009.2020688).
-
19)
-
14. Hurter, C., Ersoy, O., Telea, A.: ‘Graph bundling by kernel density estimation’, Comput. Graph. Forum, 2012, 31, (3 PART1), pp. 865–874 (doi: 10.1111/j.1467-8659.2012.03079.x).
-
20)
-
12. Blundell, R., Duncan, A.: ‘Kernel regression in empirical microeconomics’, J. Hum. Res., 1998, 33, (1), pp. 62–87 (doi: 10.2307/146315).
-
21)
-
12. Xu, H., Jagannathan, S., Lewis, F.L.: ‘Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses’, Automatica, 2012, 48, pp. 1017–1030 (doi: 10.1016/j.automatica.2012.03.007).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cps.2016.0012
Related content
content/journals/10.1049/iet-cps.2016.0012
pub_keyword,iet_inspecKeyword,pub_concept
6
6