×

Event-triggered finite-time resilient control for switched systems: an observer-based approach and its applications to a boost converter circuit system model. (English) Zbl 1422.93145

Summary: Under an event-triggered communication scheme (ETCS), this note focuses on the observer-based finite-time resilient control problem for a class of switched systems. Different from the existing finite-time problems, not only the problem of finite-time boundedness (FTBs) but also the problem of input-output finite-time stability (IO-FTSy) are considered in this paper. To effectively use the network resources, an ETCS is formulated for switched systems. Considering that not all the states could be measured, thus an event-triggered observer is constructed, and then, an observer-based resilient controller is devised, which robustly stabilizes the given systems in the meaning of finite-time control. Based on time-delay method and Lyapunov functional approach, interesting results are derived to verify the properties of the FTBs and the IO-FTSy of the event-triggered (ET) closed-loop error switched systems. All the matrix inequalities can be converted to linear matrix inequalities (LMIs) so as to simultaneously obtain the controller gain and observer gain. Finally, the applicability of the proposed control scheme is verified via a boost converter circuit system.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
Full Text: DOI

References:

[1] Liberzon, D., Morse, A.S.: Basic problems in stability and design of switched systems. IEEE Control Syst. 19(5), 59-70 (1999) · Zbl 1384.93064 · doi:10.1109/37.793443
[2] Wang, X., Zong, G.: Asynchronous finite-time dynamic output feedback control for switched time-delay systems with nonlinear disturbance. IET Control Theory Appl. 10(10), 1142-1150 (2016) · doi:10.1049/iet-cta.2015.0577
[3] Ren, H., Zong, G., Hou, L., Yi, Y.: Finite-time resilient decentralized control for interconnected impulsive switched systems with neutral delay. ISA Trans. 67, 19-29 (2017) · doi:10.1016/j.isatra.2017.01.013
[4] Li, Y., Sun, H., Zong, G.: Composite anti-disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. Int. J. Robust Nonlinear Control 27(14), 2323-2337 (2017) · Zbl 1373.93308 · doi:10.1002/rnc.3682
[5] Ren, H., Zong, G.: Input-output finite-time filtering for switched LPV systems. J. Frankl. Inst. 354(14), 6292-6311 (2017) · Zbl 1373.93298 · doi:10.1016/j.jfranklin.2017.07.039
[6] Xiong, J., Lam, J.: Stabilization of networked control systems with a logic ZOH. IEEE Trans. Autom. Control 54(2), 358-363 (2009) · Zbl 1367.93546 · doi:10.1109/TAC.2008.2008319
[7] Yan, S., Shen, M., Zhang, G.: Extended event-driven observer-based output control of networked control systems. Nonlinear Dyn. 86(3), 1639-1648 (2016) · Zbl 1371.93177 · doi:10.1007/s11071-016-2982-z
[8] Peng, C., Tian, Y.C., Tade, M.O.: State feedback controller design of networked control systems with interval time-varying delay and nonlinearity. Int. J. Robust Nonlinear Control 18(12), 1285-1301 (2008) · Zbl 1284.93111 · doi:10.1002/rnc.1278
[9] Fang, C.: Instability conditions for a class of switched linear systems with switching delays based on sampled-data analysis: applications to DC-DC converters. Nonlinear Dyn. 77(1-2), 185-208 (2014) · Zbl 1314.94119 · doi:10.1007/s11071-014-1283-7
[10] Sakthivel, R., Joby, M., Shi, P., Mathiyalagan, K.: Robust reliable sampled-data control for switched systems with application to flight control. Int. J. Syst. Sci. 47(15), 3518-3528 (2016) · Zbl 1346.93246 · doi:10.1080/00207721.2015.1090041
[11] Lian, J., Li, C., Xia, B.: Sampled-data control of switched linear systems with application to an F-18 aircraft. IEEE Trans. Ind. Electron. 64(2), 1332-1340 (2017) · doi:10.1109/TIE.2016.2618872
[12] Yue, D., Tian, E., Han, Q.: A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans. Autom. Control 58(2), 475-481 (2013) · Zbl 1369.93183 · doi:10.1109/TAC.2012.2206694
[13] Gao, L., Liao, X., Li, H., Chen, G.: Event-triggered control for multi-agent network with limited digital communication. Nonlinear Dyn. 82(4), 1659-1669 (2015) · Zbl 1348.90172 · doi:10.1007/s11071-015-2267-y
[14] Peng, C., Yang, T.C.: Event-triggered communication and \[{H}_\infty H\]∞ control co-design for networked control systems. Automatica 49(5), 1326-1332 (2013) · Zbl 1319.93022 · doi:10.1016/j.automatica.2013.01.038
[15] Xu, S., Lam, J.: On equivalence and efficiency of certain stability criteria for time-delay systems. IEEE Trans. Autom. Control 52(1), 95-101 (2007) · Zbl 1366.93451 · doi:10.1109/TAC.2006.886495
[16] Xu, S., Lam, J., Ho, D.W.C.: A new lmi condition for delay-dependent asymptotic stability of delayed hopfield neural networks. IEEE Trans. Circ. Syst. II Express Briefs 53(3), 230-234 (2006) · doi:10.1109/TCSII.2005.857764
[17] Qi, W., Zong, G., Karimi, H.R., L.: Control for positive delay systems with semi-Markov process and application to a communication network model, IEEE Trans. Ind. Electron. https://doi.org/10.1109/TIE.2018.2838113
[18] Xu, S., Lam, J., Mao, X.: Delay-dependent \[h_{\infty }\] h∞ control and filtering for uncertain markovian jump systems with time-varying delays. IEEE Trans. Circ. Syst. I Regul. Pap. 54(9), 2070-2077 (2007) · Zbl 1374.93134 · doi:10.1109/TCSI.2007.904640
[19] Zhang, H., Feng, G., Yan, H., Chen, Q.: Observer-based output feedback event-triggered control for consensus of multi-agent systems. IEEE Trans. Ind. Electron. 61(9), 4885-4894 (2014) · doi:10.1109/TIE.2013.2290757
[20] Chen, P., Zhang, J.: Event-triggered output-feedback \[{H}_\infty H\]∞ control for networked control systems with time-varying sampling. IET Control Theory Appl. 9(9), 1384-1391 (2015) · doi:10.1049/iet-cta.2014.0876
[21] Liu, J., Zha, L., Xie, X., Tian, E.: Observer-based event-triggered control for certain and uncertain linear systems. Nonlinear Dyn. 91(3), 2049-2061 (2018) · Zbl 1390.93327 · doi:10.1007/s11071-017-4002-3
[22] Li, T., Fu, J.: Event-triggered control of switched linear systems. J. Frankl. Inst. 354(15), 6451-6462 (2017) · Zbl 1373.93216 · doi:10.1016/j.jfranklin.2017.05.018
[23] Ma, G., Liu, X., Qin, L., Wu, G.: Finite-time event-triggered \[{H}_\infty H\]∞ control for switched systems with time-varying delay. Neurocomputing 207, 828-842 (2016) · doi:10.1016/j.neucom.2016.05.070
[24] Weiss, L., Infante, E.: Finite time stability under perturbing forces and on product spaces. IEEE Trans. Autom. Control 12(1), 54-59 (1967) · Zbl 0168.33903 · doi:10.1109/TAC.1967.1098483
[25] Zong, G., Ren, H., Hou, L.: Finite-time stability of interconnected impulsive switched systems. IET Control Theory Appl. 10(6), 648-654 (2016) · doi:10.1049/iet-cta.2015.0617
[26] Sakthivel, R., Saravanakumar, T., Ma, Y.-K., Marshal Anthoni, S.: Finite-time resilient reliable sampled-data control for fuzzy systems with randomly occurring uncertainties. Fuzzy Sets Syst. 329, 1-18 (2017) · Zbl 1381.93067 · doi:10.1016/j.fss.2017.02.007
[27] Sakthivel, R., Santra, S., Kaviarasan, B., Park, J.H.: Finite-time sampled-data control of permanent magnet synchronous motor systems. Nonlinear Dyn. 86(3), 2081-2092 (2016) · Zbl 1371.93157 · doi:10.1007/s11071-016-3017-5
[28] Zong, G., Wang, R., Zheng, W., Hou, L.: Finite-time \[{H}_\infty H\]∞ control for discrete-time switched nonlinear systems with time delay. Int. J. Robust Nonlinear Control 25(6), 914-936 (2015) · Zbl 1309.93057 · doi:10.1002/rnc.3121
[29] Liu, X., Yu, X., Zhou, X., Xi, H.: Finite-time \[{H}_{\infty }H\]∞ control for linear systems with semi-Markovian switching. Nonlinear Dyn. 85(4), 2297-2308 (2016) · Zbl 1349.93140 · doi:10.1007/s11071-016-2829-7
[30] Amato, F., Ambrosino, R., Cosentino, C., De Tommasi, G.: Input-output finite time stabilization of linear systems. Automatica 46(9), 1558-1562 (2010) · Zbl 1202.93142 · doi:10.1016/j.automatica.2010.06.005
[31] Amato, F., Carannante, G., De Tommasi, G., Pironti, A.: Input-output finite-time stability of linear systems: necessary and sufficient conditions. IEEE Trans. Autom. Control 57(12), 3051-3063 (2012) · Zbl 1369.93556 · doi:10.1109/TAC.2012.2199151
[32] Amato, F., De Tommasi, G., Pironti, A.: Input-output finite-time stabilization of impulsive linear systems: necessary and sufficient conditions. Nonlinear Anal. Hybrid Syst. 19, 93-106 (2016) · Zbl 1329.93122 · doi:10.1016/j.nahs.2015.08.005
[33] Ren, H., Zong, G., Li, T.: Event-triggered finite-time control for networked switched linear systems with asynchronous switching. IEEE Trans. Syst. Man. Cybern. Syst. https://doi.org/10.1109/TSMC.2017.2789186 · doi:10.1109/TSMC.2017.2789186
[34] Ren, H., Zong, G.: Robust input-output finite-time filtering for uncertain Markovian jump nonlinear systems with partially known transition probabilities. Int. J. Adapt. Control Signal Process. 31(10), 1455-1473 (2017) · Zbl 1376.93108 · doi:10.1002/acs.2777
[35] Wen, S., Zeng, Z., Huang, T.: Observer-based \[{H}_\infty H\]∞ control of discrete time-delay systems with random communication packet losses and multiplicative noises. Appl. Math. Comput. 219(12), 6484-6493 (2013) · Zbl 1284.93219
[36] Xiang, Z., Sun, Y.N., Mahmoud, M.S.: Robust finite-time \[{H}_\infty H\]∞ control for a class of uncertain switched neutral systems. Commun. Nonlinear Sci. Numer. Simul. 17(4), 1766-1778 (2012) · Zbl 1239.93036 · doi:10.1016/j.cnsns.2011.09.022
[37] Seuret, A., Gouaisbaut, F.: Wirtinger-based integral inequality: application to time-delay systems. Automatica 49(9), 2860-2866 (2013) · Zbl 1364.93740 · doi:10.1016/j.automatica.2013.05.030
[38] Ho, D.W.C., Lu, G.: Robust stabilization for a class of discrete-time non-linear systems via output feedback: the unified lmi approach. Int. J. Control 76(2), 105-115 (2003) · Zbl 1026.93048 · doi:10.1080/0020717031000067367
[39] Peng, C., Ma, S., Xie, X.: Observer-based non-pdc control for networked TS fuzzy systems with an event-triggered communication. IEEE Trans. Cybern. 47(8), 2279-2287 (2017) · doi:10.1109/TCYB.2017.2659698
[40] Sreekumar, C., Agarwal, V.: A hybrid control algorithm for voltage regulation in DC-DC boost converter. IEEE Trans. Ind. Electron. 55(6), 2530-2538 (2008) · doi:10.1109/TIE.2008.918640
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.