×

Extended dissipativity and event-triggered synchronization for T-S fuzzy Markovian jumping delayed stochastic neural networks with leakage delays via fault-tolerant control. (English) Zbl 1436.93004

Summary: This paper concentrates on the extended dissipativity and event-triggered synchronization for T-S fuzzy Markovian jumping delayed stochastic neural networks with leakage delays and fault-tolerant control. We present an event-triggered communication scheme, which utilizes the effect of transmission delay with different failure rates. After giving a foundation to the stochastic model, the paper establishes some fundamental results on quadratically stable and extended dissipativity utilizing the Lyapunov functional, free-weight matrices, as well as the relationship between time-varying delay and leakage delays. The explicit expression of the desired controller gains and event-triggered parameters can be obtained by solving the established LMIs. The novel extended dissipative inequality contains several weighting matrices, by converting the weighting matrices in a new performance index, and the extended dissipativity will be degraded to the \(H_{\infty }\) performance, \(L_2-L_{\infty }\) performance, passivity and dissipativity, respectively. Finally, interesting numerical examples are given to show the effectiveness of the theoretical results.

MSC:

93A14 Decentralized systems
93C43 Delay control/observation systems
93E03 Stochastic systems in control theory (general)
60J76 Jump processes on general state spaces
93C42 Fuzzy control/observation systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ali, Ms; Saravanakumar, R.; Ahn, Ck; Karimi, Hr, Stochastic \(H_{\infty }\) filtering for neural networks with leakage delay and mixed time-varying delays, Inform Sci, 388-389, 118-134 (2017) · Zbl 1432.93356
[2] Ali, Ms; Gunasekaran, N.; Zhu, Q., State estimation of T-S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control, Fuzzy Sets Syst, 306, 87-104 (2017) · Zbl 1368.93672
[3] Arik, S., An improved robust stability result for uncertain neural networks with multiple time delays, Neural Netw, 54, 1-10 (2014) · Zbl 1307.93313
[4] Balasubramaniam, P.; Ali, Ms; Arik, S., Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays, Expert Syst Appl, 37, 7737-7744 (2010)
[5] Cichocki, A.; Unbehauen, R., Neural networks for optimization and signal processing (1993), Chichester: Wiley, Chichester · Zbl 0824.68101
[6] Fang, S.; Jiang, M.; Wang, X., Exponential convergence estimates for neural networks with discrete and distributed delays, Nonlinear Anal Real World Appl, 10, 702-714 (2009) · Zbl 1167.34378
[7] Feng, Z.; Lam, J., Stability and dissipativity analysis of distributed delay cellular neural networks, IEEE Trans Neural Netw, 22, 976-981 (2011)
[8] Feng, Z.; Shi, P., Admissibilization of singular interval-valued fuzzy systems, IEEE Trans Fuzzy Syst, 25, 1765-1776 (2017)
[9] Gopalsamy, K., Stability and oscillations in delay differential equations of population dynamics (1992), Dordrecht: Kluwer Academic Publishers, Dordrecht · Zbl 0752.34039
[10] Gopalsamy, K., Leakage delays in BAM, J Math Anal Appl, 325, 1117-1132 (2007) · Zbl 1116.34058
[11] Guan, W.; Liu, F., Finite-time dissipative control for singular T-S fuzzy Markovian jump systems under actuator saturation with partly unknown transition rates, Neurocomputing, 207, 60-70 (2016)
[12] Hu, S.; Yin, X.; Zhang, Y.; Tian, Eg, Event-triggered guaranteed cost control for uncertain discrete-time networked control systems with time-varying transmission delays, IET Control Theory Appl, 6, 2793-2804 (2012)
[13] Jeltsema, D.; Scherpen, Jma, Tuning of passivity-preserving controllers for switched-mode power converters, IEEE Trans Autom Control, 48, 1333-1344 (2004) · Zbl 1365.93184
[14] Kao, Yg; Wang, Ch; Xie, J.; Karimi, Hr; Li, W., \(H_{\infty }\) sliding mode control for uncertain neutral-type stochastic systems with Markovian jumping parameters, Inform Sci, 314, 200-211 (2015) · Zbl 1386.93063
[15] Kovacic, M., Markovian neural networks, Biol Cybern, 64, 337-342 (1991) · Zbl 0722.90060
[16] Lee, Th; Park, Mj; Park, Jh; Kwon, Om; Lee, Sm, Extended dissipative analysis for neural networks with time-varying delays, IEEE Trans Neural Netw Learn Syst, 25, 1936-1941 (2014)
[17] Li, X.; Cao, J., Delay-dependent stability of neural networks of neutral type with time delay in the leakage term, Nonlinearity, 23, 1709-1726 (2010) · Zbl 1196.82102
[18] Li, T.; Luo, Q.; Sun, Cy; Zhang, By, Exponential stability of recurrent neural networks with time-varying discrete and distributed delays, Nonlinear Anal Real World Appl, 10, 2581-2589 (2009) · Zbl 1163.92302
[19] 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, 1825-1834 (2014) · Zbl 1296.93200
[20] Li, B.; Wang, Z.; Ma, L., An event-triggered pinning control approach to synchronization of discrete-time stochastic complex dynamical networks, IEEE Trans Neural Netw Learn Syst, 29, 5812-5822 (2018)
[21] Li, W.; Wang, Z.; Liu, Q.; Guo, L., An information aware event-triggered scheme for particle filter based remote state estimation, Automatica, 103, 151-158 (2019) · Zbl 1415.93251
[22] Liu, H.; Wang, Z.; Shen, B.; Liu, X., Event-triggered \(H_{\infty }\) state estimation for delayed stochastic memristive neural networks with missing measurements: the discrete time case, IEEE Trans Neural Netw Learn Syst, 29, 3726-3737 (2018)
[23] Ma, H.; Li, H.; Liang, H.; Dong, G., Adaptive fuzzy event-triggered control for stochastic nonlinear systems with full state constraints and actuator faults, IEEE Trans Fuzzy Syst (2019) · doi:10.1109/TFUZZ.2019.2896843
[24] Mao, X., Stochastic differential equations with their applications (1997), Chichester: Horwood, Chichester · Zbl 0892.60057
[25] Mao, Z.; Jiang, B.; Shi, P., \(H_{\infty }\) fault detection filter design for networked control systems modelled by discrete Markovian jump systems, IET Control Theory Appl, 1, 1336-1343 (2007)
[26] Niu, Y.; Wang, X.; Lu, J., Dissipative-based adaptive neural control for nonlinear systems, J Control Theory Appl, 2, 126-130 (2004) · Zbl 1260.93093
[27] Pecora, Lm; Carroll, Tl, Synchronization in chaotic systems, Phys Rev Lett, 64, 821-824 (1990) · Zbl 0938.37019
[28] Peng, C.; Yang, Tc, Event-triggered communication and \(H_{\infty }\) control co-design for networked control systems, Automatica, 49, 1326-1332 (2013) · Zbl 1319.93022
[29] Qiu, J.; Tian, H.; Lu, Q.; Gao, H., Nonsynchronized robust filtering design for continuous-time T-S fuzzy affine dynamic systems based on piecewise Lyapunov functions, IEEE Trans Cybern, 43, 1755-1766 (2013)
[30] Sakthivel, R.; Selvaraj, P.; Mathiyalagan, K.; Park, Jh, Robust fault-tolerant \(H_{\infty }\) control for offshore steel jacket platforms via sampled-data approach, J Franklin Inst, 352, 2259-2279 (2015) · Zbl 1395.93198
[31] Sakthivel, R.; Selvi, S.; Mathiyalagan, K., Fault-tolerant sampled-data control of flexible spacecraft with probabilistic time delays, Nonlinear Dyn, 79, 1835-1846 (2015) · Zbl 1331.93146
[32] Selvaraj, P.; Sakthivel, R.; Marshal Anthoni, S.; Rathika, M.; Y. Cheol, M., Dissipative sampled-data control of uncertain nonlinear systems with time-varying delays, Complexity, 21, 142-154 (2016)
[33] Senan, S.; Ali, Ms; Vadivel, R.; Arik, S., Decentralized event-triggered synchronization of uncertain Markovian jumping neutral-type neural networks with mixed delays, Neural Netw, 86, 32-41 (2017) · Zbl 1429.93010
[34] Sheng, L.; Wang, Z.; Zou, L.; Alsaadi, Fe, Event-based \(H_{\infty }\) state estimation for time-varying stochastic dynamical networks with state- and disturbance-dependent noises, IEEE Trans Neural Netw Learn Syst, 28, 2382-2394 (2017)
[35] Shu, Z.; Lam, J., Global exponential estimates of stochastic interval neural networks with discrete and distributed delays, Neurocomputing, 71, 2950-2963 (2008)
[36] Syed, Am, Stability of Markovian jumping recurrent neural networks with discrete and distributed time varying delays, Neurocomputing, 149, 1280-1285 (2015)
[37] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Trans Syst Man Cybern, 15, 116-132 (1985) · Zbl 0576.93021
[38] Tan, Y.; Du, D.; Qi, Q., State estimation for Markovian jump systems with an event-triggered communication scheme, Circuits Syst Signal Process, 36, 2-24 (2017) · Zbl 1368.94039
[39] Tong, D.; Zhou, W.; Zhou, X.; Yang, J.; Xu, Y., Exponential synchronization for stochastic neural networks with multi-delayed and Markovian switching via adaptive feedback control, Commun Nonlinear Sci Numer Simul, 29, 359-371 (2015) · Zbl 1510.68101
[40] Tong, D.; Rao, P.; Chen, Q.; Ogorzalek, Mj; Li, X., Exponential synchronization and phase locking of a multilayer Kuramoto-oscillator system with a pacemaker, Neurocomputing, 308, 129-137 (2018)
[41] Wang, S.; Feng, J.; Zhang, H., Robust fault tolerant control for a class of networked control systems with state delay and stochastic actuator failures, Int J Adapt Control Signal Process, 28, 798-811 (2014) · Zbl 1327.93147
[42] Wang, H.; Shi, P.; Lim, C.; Xue, Q., Event-triggered control for networked Markovian jump systems, Int J Robust Nonlinear, 25, 3422-3438 (2015) · Zbl 1338.93348
[43] Wei, H.; Li, R.; Chen, C.; Tu, Z., Extended dissipative analysis for memristive neural networks with two additive time-varying delay components, Neurocomputing, 216, 429-438 (2016)
[44] Wen, S.; Zeng, Z.; Chen, Mzq; Huang, T., Synchronization of switched neural networks with communication delays via the event-triggered control, IEEE Trans Neural Netw Learn Syst, 28, 2334-2343 (2017)
[45] Wu, Zg; Lam, J.; Su, H.; Chu, J., Stability and dissipativity analysis of static neural networks with time delay, IEEE Trans Neural Netw Learn Syst, 23, 199-210 (2012)
[46] Xiao, J.; Li, Y.; Zhong, S.; Xu, F., Extended dissipative state estimation for memristive neural networks with time-varying delay, ISA Trans, 64, 113-128 (2016)
[47] Xu, C.; Tong, D.; Chen, Q.; Zhou, W.; Shi, P., Exponential stability of Markovian jumping systems via adaptive sliding mode control, IEEE Trans Syst Man Cybern Syst (2019) · doi:10.1109/TSMC.2018.2884565
[48] Yue, D.; Tian, E.; Zhang, Y.; Peng, C., Delay-distribution dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay, IEEE Trans Syst Man Cybern Syst Part B Cybern, 39, 503-516 (2009)
[49] Zeng, Hb; Park, Jh; Zhang, Cf; Wang, W., Stability and dissipativity analysis of static neural networks with interval time-varying delay, J Franklin Inst, 352, 1284-1295 (2015) · Zbl 1307.93446
[50] Zeng, Hb; He, Y.; Shi, P.; Wu, M.; Xiao, Sp, Dissipativity analysis of neural networks with time-varying delays, Neurocomputing, 168, 741-746 (2015)
[51] Zeng, N.; Zhang, H.; Liu, W.; Liang, J.; Alsaadi, Fe, A switching delayed PSO optimized extreme learning machine for short-term load forecasting, Neurocomputing, 240, 175-182 (2017)
[52] Zeng, N.; Qiu, H.; Wang, Z.; Liu, W.; Li, Y., A new switching-delayed-PSO-based optimized SVM algorithm for diagnosis of Alzheimer’s disease, Neurocomputing, 320, 195-202 (2018)
[53] Zhang, Xm; Han, Ql, Event-triggered dynamic output feedback control for networked control systems, IET Control Theory Appl, 8, 226-234 (2014)
[54] Zhang, J.; Peng, C., Synchronization of master-slave neural networks with a decentralized event triggered communication scheme, Neurocomputing, 173, 1824-1831 (2016)
[55] Zhang, B.; Zheng, Wx; Xu, S., Filtering of Markovian jump delay systems based on a new performance index, IEEE Trans Circuits Syst, I, 60, 1250-1263 (2013) · Zbl 1468.94288
[56] Zheng, C.; Zhang, X.; Wang, Z., Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays, ISA Trans, 56, 8-17 (2015)
[57] Zhu, Q.; Cao, J., Stability analysis for stochastic neural networks of neutral-type with both Markovian jump parameters and mixed time delays, Neurocomputing, 73, 2671-2680 (2010)
[58] Zhu, Q.; Cao, J.; Hayat, T.; Alsaadi, F., Robust stability of Markovian jump stochastic neural networks with time delays in the leakage terms, Neural Process Lett, 41, 1-27 (2013)
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.