Non-fragile memory filtering of T-S fuzzy delayed neural networks based on switched fuzzy sampled-data control. (English) Zbl 1452.93021
Summary: This paper deals with the non-fragile memory filtering issue of T-S fuzzy delayed neural networks with randomly occurring time-varying parameters uncertainties and variable sampling rates. Compared with existing sampled-data control schemes, an improved switched fuzzy memory sampled-data control protocol is designed for the first time, which involves not only a signal transmission delay but also switched topologies. By developing some new terms and taking full advantage of the variable characteristics related to the actual sampling pattern, a modified loose-looped fuzzy membership functions (FMFs) dependent Lyapunov-Krasovskii functional (LKF) is constructed based on the information of the time derivative of FMFs. Meanwhile, some relaxed matrices chosen in LKF are not consequentially positive definite. Moreover, with the LKF methodology and employing the developed estimation technique, several optimized control algorithms with both a larger sampling period and upper bound of time-varying delays for achieving the stabilization of the resultant T-S fuzzy delayed neural networks are derived. Finally, a numerical example is presented to demonstrate the superiority and applicability of the theoretical results.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93E11 | Filtering in stochastic control theory |
| 93A14 | Decentralized systems |
| 93C57 | Sampled-data control/observation systems |
Keywords:
T-S fuzzy neural networks; switched fuzzy sampled-data control; non-fragile memory filtering; fuzzy membership functionReferences:
| [1] | Egmont-Petersen, M.; Ridder, D. D.; Handels, H., Image processing with neural networks-a review, Pattern Recognit., 35, 10, 2279-2301 (2002) · Zbl 1006.68884 |
| [2] | Zhang, T. P.; Fang, B.; Tang, Y. Y.; He, G. H.; Wen, J., Topology preserving non-negative matrix factorization for face recognition, IEEE Trans. Image Process., 17, 4, 574-584 (2008) |
| [3] | Hosseini, A.; Wang, J.; Hosseini, S. M., A recurrent neural network for solving a class of generalized convex optimization problems, Neural Netw., 44, 78-86 (2013) · Zbl 1296.90088 |
| [4] | Jiang, M. H.; Gielen, G.; Deng, B. X.; Zhu, X. Y., A fast learning algorithm for time-delay neural networks, Inf. Sci., 148, 27-39 (2002) · Zbl 1024.68082 |
| [5] | Faydasicok, O.; Arik, S., A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks, Neural Netw., 44, 64-71 (2013) · Zbl 1296.92085 |
| [6] | Arik, S., New criteria for global robust stability of delayed neural networks with norm-bounded uncertainties, IEEE Trans. Neural Netw. Learn. Syst., 25, 1045-1052 (2014) |
| [7] | Wu, Z. G.; Shi, P.; Su, H. Y.; Chu, J., Local synchronization of chaotic neural networks with sampled-data and saturating actuators, IEEE Trans. Cybern., 44, 12, 2635-2645 (2014) |
| [8] | Lee, T. H.; Park, M. J.; Park, J. H.; Kwon, O. M.; Lee, S. M., Extended dissipative analysis for neural networks with time-varying delays, IEEE Trans. Neural Netw. Learn. Syst., 25, 10, 1936-1941 (2014) |
| [9] | Liu, X. Z.; Zhang, K. X.; Xie, W. C., Pinning impulsive synchronization of reaction-diffusion neural networks with time-varying delays, IEEE Trans. Neural Netw. Learn. Syst., 28, 5, 1055-1067 (2017) |
| [10] | Zhang, C. K.; He, Y.; Jiang, L.; Wu, M., Stability analysis for delayed neural networks considering both conservativeness and complexity, IEEE Trans. Neural Netw. Learn. Syst., 27, 7, 1486-1501 (2016) |
| [11] | Chen, W. H.; Lu, X. M.; Zheng, W. X., Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks, IEEE Trans. Neural Netw. Learn. Syst., 26, 4, 734-748 (2015) |
| [12] | He, Y.; Ji, M. D.; Zhang, C. K.; Wu, M., Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality, Neural Netw., 77, 80-86 (2016) · Zbl 1417.34174 |
| [13] | Shi, K. B.; Liu, X. Z.; Tang, Y. Y.; Zhu, H.; Zhong, S. M., Some novel approaches on state estimation of delayed neural networks, Inf. Sci., 372, 313-331 (2016) · Zbl 1429.93142 |
| [14] | Shen, H.; Zhu, Y. Z.; Zhang, L. X.; Park, J. H., Extended dissipative state estimation for markov jump neural networks with unreliable links, IEEE Trans. Neural Netw. Learn. Syst., 28, 2, 346-358 (2017) |
| [15] | Cheng, J.; Park, J. H.; Karimi, H. R.; Shen, H., A flexible terminal approach to sampled-data exponentially synchronization of Markovian neural networks with time-varying delayed signals, IEEE Trans. Cybern., 48, 8, 2232-2244 (2018) |
| [16] | Saravanakumar, R.; Rajchakit, G.; Ahn, C. K.; Karimi, H. R., Exponential stability, passivity, and dissipativity analysis of generalized neural networks with mixed time-varying delays, IEEE Trans. Syst. Man Cybern. Syst., 99, 1-11 (2017) |
| [17] | Arik, S., An improved robust stability result for uncertain neural networks with multiple time delays, Neural Netw., 54, 1-10 (2014) · Zbl 1307.93313 |
| [18] | Senan, S.; Ali, M. S.; 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 |
| [19] | Wen, S. P.; Zeng, Z. G.; Chen, M. Z.Q.; Huang, T. W., Synchronization of switched neural networks with communication delays via the event-triggered control, IEEE Trans. Neural Netw. Learn. Syst., 28, 10, 2334-2343 (2017) |
| [20] | Zhang, R. M.; Zeng, D. Q.; Zhong, S. M.; Yu, Y. B., Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays, Appl. Math. Comput., 310, 57-74 (2017) · Zbl 1426.94180 |
| [21] | Liu, Y. J.; Guo, B. Z.; Park, J. H., Non-fragile \(H_\infty\) filtering for delayed Takagi-Sugeno fuzzy systems with randomly occurring gain variations, Fuzzy Sets Syst., 316, 99-116 (2017) · Zbl 1392.93048 |
| [22] | Lu, R. Q.; Shi, P.; Su, H. Y.; Wu, Z. G.; Lu, J. Q., Synchronization of general chaotic neural networks with nonuniform sampling and packet missing: a switched system approach, IEEE Trans. Neural Netw. Learn. Syst., 29, 3, 523-533 (2018) |
| [23] | Shi, K. B.; Wang, J.; Zhong, S. M.; Zhang, X. J.; Liu, Y. J.; Cheng, J., New reliable nonuniform sampling control for uncertain chaotic neural networks under Markov switching topologies, Appl. Math. Comput., 347, 169-193 (2019) · Zbl 1428.92015 |
| [24] | Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE Trans. Syst. Man Cybern. Syst., 15, 1, 116-132 (1985) · Zbl 0576.93021 |
| [25] | Liu, Y. J.; Lee, S. M., Stability and stabilization of Takagi-Sugeno fuzzy systems via sampled-data and state quantized controller, IEEE Trans. Fuzzy Syst., 24, 1, 635-644 (2016) |
| [26] | Wang, Z. P.; Wu, H. N., Fuzzy impulsive control for uncertain nonlinear systems with guaranteed cost, Fuzzy Sets Syst., 302, 143-162 (2016) · Zbl 1378.93070 |
| [27] | Li, H. Y.; Pan, Y. N.; Zhou, Q., Filter design for interval type-2 fuzzy systems with D stability constraints under a unified frame, IEEE Trans. Fuzzy Syst., 23, 3, 719-725 (2015) |
| [28] | Sakthivel, R.; Selvi, S.; Mathiyalagan, K.; Shi, P., Reliable mixed \(H_\infty\) and passivity-based control for fuzzy markovian switching systems with probabilistic time delays and actuator failures, IEEE Trans. Cybern., 23, 3, 2720-2731 (2015) |
| [29] | Cheng, J.; Park, J. H.; Liu, Y. J.; Liu, Z. J.; Tang, L. M., Finite-time \(H_\infty\) fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions, Fuzzy Sets Syst., 314, 99-115 (2017) · Zbl 1368.93147 |
| [30] | Shen, H.; Li, F.; Yan, H.; Karimi, H. R.; Lam, H. K., Finite-time event-triggered \(H_\infty\) control for T-S fuzzy Markov jump systems, IEEE Trans. Fuzzy Syst., 26, 5, 3122-3135 (2018) |
| [31] | Sakthivel, R.; Saravanakumar, T.; Kaviarasan, B.; Lim, Y. D., Finite-time dissipative based fault-tolerant control of Takagi-Sugeno fuzzy systems in a network environment, J. Franklin Inst., 354, 8, 3430-3455 (2017) · Zbl 1364.93423 |
| [32] | Liu, Y. J.; Guo, B. Z.; Park, J. H.; Lee, S., Event-based reliable dissipative filtering for T-S fuzzy systems with asynchronous constraints, IEEE Trans. Fuzzy Syst., 26, 4, 2089-2098 (2018) |
| [33] | Wang, Y. Y.; Shen, H.; Karimi, H. R.; Duan, D. P., Dissipativity-based fuzzy integral sliding mode control of continuous-time T-S fuzzy systems, IEEE Trans. Fuzzy Syst., 26, 3, 1164-1176 (2018) |
| [34] | Liu, Y. J.; Park, J. H.; Guo, B. Z.; Shu, Y. J., Further results on stabilization of chaotic systems based on fuzzy memory sampled-data control, IEEE Trans. Fuzzy Syst., 26, 2, 1040-1045 (2018) |
| [35] | Ahn, C. K., Delay-dependent state estimation for T-S fuzzy delayed Hopfield neural networks, Nonlinear Dyn., 61, 3, 483-489 (2010) · Zbl 1204.93047 |
| [36] | Balasubramaniam, P.; Vembarasan, V.; Rakkiyappan, R., Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays, Commun. Nonlinear Sci. Numer. Simul., 16, 2109-2129 (2011) · Zbl 1221.93254 |
| [37] | Long, S. J.; Xu, D. Y., Global exponential p-stability of stochastic non-autonomous Takagi-Sugeno fuzzy cellular neural networks with time-varying delays and impulses, Fuzzy Sets Syst., 253, 82-100 (2014) · Zbl 1338.93212 |
| [38] | Samidurai, R.; Senthilraj, S.; Zhu, Q. X.; Raja, R.; Hu, W., Effects of leakage delays and impulsive control in dissipativity analysis of Takagi-Sugeno fuzzy neural networks with randomly occurring uncertainties, J. Franklin Inst., 354, 8, 3574-3593 (2017) · Zbl 1364.93424 |
| [39] | Ahn, C. K., Passive and exponential filter design for fuzzy neural networks, Inf. Sci., 238, 126-137 (2013) · Zbl 1320.93056 |
| [40] | Shi, P.; Zhang, Y. Q.; Chadli, M.; Agarwal, R. K., Dissipativity analysis for discrete time-delay fuzzy neural networks with markovian jumps, IEEE Trans. Fuzzy Syst., 24, 2, 432-433 (2016) |
| [41] | Wang, Y. Y.; Karimi, H. R.; Lam, H. K.; Shen, H., An improved result on exponential stabilization of sampled-data fuzzy systems, IEEE Trans. Fuzzy Syst., 26, 6, 3875-3883 (2018) |
| [42] | Shi, K. B.; Liu, X. Z.; Zhu, H.; Zhong, S. M.; Liu, Y. J.; Yin, C., Novel integral inequality approach on master-slave synchronization of chaotic delayed Lur’e systems with sampled-data feedback control, Nonlinear Dyn., 83, 3, 1259-1274 (2016) · Zbl 1351.93061 |
| [43] | Lee, T. H.; Park, J. H., Improved criteria for sampled-data synchronization of chaotic Lur’e systems using two new approaches, Nonlinear Anal. Hybrid Syst., 24, 132-145 (2017) · Zbl 1377.93103 |
| [44] | Lu, R. Q.; Shi, P.; Su, H. Y.; Wu, Z. G.; Lu, J. Q., Synchronization of general chaotic neural networks with nonuniform sampling and packet missing: a switched system approach, IEEE Trans. Neural Netw. Learn. Syst., 29, 3, 523-533 (2018) |
| [45] | Zhang, R. M.; Liu, X. Z.; Zeng, D. Q.; Zhong, S. M.; Shi, K. B., A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems, Fuzzy Sets Syst., 344, 108-128 (2018) · Zbl 1397.93229 |
| [46] | Zhang, R. M.; Zeng, D. Q.; Zhong, S. M.; Shi, K. B.; Cui, J. Z., New approach on designing stochastic sampled-data controller for exponential synchronization of chaotic Lur’e systems, Nonlinear Anal. Hybrid Syst., 29, 303-321 (2018) · Zbl 1388.93059 |
| [47] | Yucel, E.; Ali, M. S.; Gunasekaran, N.; Arik, S., Sampled-data filtering of Takagi-Sugeno fuzzy neural networks with interval time-varying delays, Fuzzy Sets Syst., 316, 69-81 (2017) · Zbl 1392.93031 |
| [48] | Ali, M. S.; Gunasekaran, N.; Zhu, Q. X., 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 |
| [49] | Shi, K. B.; Wang, J.; Tang, Y. Y.; Zhong, S. M., Reliable asynchronous sampled-data filtering of T-S fuzzy uncertain delayed neural networks with stochastic switched topologies, Fuzzy Sets Syst. (2019) |
| [50] | Liu, Y. J.; Guo, B. Z.; Park, J. H.; Lee, S. L., Nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control, IEEE Trans. Neural Netw. Learn. Syst., 29, 1, 118-128 (2018) |
| [51] | McKernana, A.; Sala, A.; Ariño, C.; Irwin, G. W., Sampled-data gain scheduling of continuous LTV plants, Automatica, 45, 2451-2453 (2009) · Zbl 1183.93094 |
| [52] | Zhu, X. L.; Lin, H.; Xie, X. P., Sampled-data fuzzy stabilization of nonlinear systems under nonuniform sampling, IEEE Trans. Fuzzy Syst., 24, 6, 1654-1667 (2016) |
| [53] | Peng, C.; Yue, D.; Fei, M. R., Relaxed stability and stabilization conditions of networked fuzzy control systems subject to asynchronous grades of membership, IEEE Trans. Fuzzy Syst., 22, 5, 1101-1112 (2014) |
| [54] | Liu, K.; Fridman, E., Wirtinger’s inequality and Lyapunov-based sampled-data stabilization, Automatica, 48, 1, 102-108 (2012) · Zbl 1244.93094 |
| [55] | Liu, K.; Fridman, E., Networked-based stabilization via discontinuous Lyapunov functionals, Int. J. Robust Nonlinear Control, 22, 420-436 (2012) · Zbl 1261.93071 |
| [56] | Seuret, A.; Gouaisbaut, F., Wirtinger-based integral inequality: application to time-delay systems, Automatica, 49, 2860-2866 (2013) · Zbl 1364.93740 |
| [57] | Zhang, X. M.; Han, Q. L., State estimation for static neural networks with time-varying delays based on an improved reciprocally convex inequality, IEEE Trans. Neural Netw. Learn. Syst., 29, 4, 1376-1381 (2018) |
| [58] | Zeng, H. B.; Teo, K. L.; He, Y., A new looped-functional for stability analysis of sampled-data systems, Automatica, 82, 328-331 (2017) · Zbl 1372.93153 |
| [59] | Wang, L. K.; Lam, H. K., A new approach to stability and stabilization analysis for continuous-time Takagi-Sugeno fuzzy systems with time delay, IEEE Trans. Fuzzy Syst., 26, 4, 2460-2465 (2018) |
| [60] | Wang, Y. Y.; Xia, Y. Q.; Zhou, P. F., Fuzzy-model-based sampled-data control of chaotic systems: a fuzzy time-dependent Lyapunov-Krasovskii functional approach, IEEE Trans. Fuzzy Syst., 25, 6, 1672-1684 (2017) |
| [61] | Sakthivela, R.; Saravanakumar, T.; Ma, Y. K.; Anthoni, S. M., Finite-time resilient reliable sampled-data control for fuzzy systems with randomly occurring uncertainties, Fuzzy Sets Syst., 329, 1-18 (2017) · Zbl 1381.93067 |
| [62] | Ali, M. S.; Meenakshi, K.; Gunasekaran, N.; Usha, M., Finite-time passivity of discrete-time T-S fuzzy neural networks with time-varying delays, Iran. J. Fuzzy Syst., 15, 4, 93-107 (2018) · Zbl 1400.93165 |
| [63] | Cheng, J.; Park, J. H.; Cao, J.; Zhang, D., Quantized \(H_\infty\) filtering for switched linear parameter-varying systems with sojourn probabilities and unreliable communication channels, Inf. Sci., 466, 289-302 (2018) · Zbl 1448.93323 |
| [64] | Lian, Z.; He, Y.; Zhang, C. K.; Shi, P.; Wu, M., Robust \(H_\infty\) control for T-S fuzzy systems with state and input time-varying delays via delay-product-type functional method, IEEE Trans. Fuzzy Syst. (2018) |
| [65] | Xiao, J. Y.; Zhong, S. M., Extended dissipative conditions for memristive neural networks with multiple time delays, Appl. Math. Comput., 323, 145-163 (2018) · Zbl 1430.92008 |
| [66] | Zeng, H. B.; Teo, K. L.; He, Y.; Wang, W., Sampled-data-based dissipative control of T-S fuzzy systems, Appl. Math. Model., 65, 415-427 (2019) · Zbl 1481.93075 |
| [67] | Ali, M. S.; Usha, M.; Cao, J. D.; Lu, G. P., Synchronisation analysis for stochastic T-S fuzzy complex networks with coupling delay, Int. J. Syst. Sci., 50, 3, 585-598 (2019) · Zbl 1482.93598 |
| [68] | Ding, Y. C.; Zhong, S. M.; Long, S. H., Asymptotic stability in probability of singular stochastic systems with Markovian switchings, Int. J. Robust Nonlinear Control, 27, 4312-4322 (2017) · Zbl 1379.93095 |
| [69] | Mathiyalagan, K.; Anbuvithya, R.; Sakthivel, R.; Park, J. H.; Prakash, P., Non-fragile \(H_\infty\) synchronization of memristor-based neural networks using passivity theory, Neural Netw., 74, 85-100 (2016) · Zbl 1398.34109 |
| [70] | Xiao, J.; Li, Y. T.; Zhong, S. M.; Xu, F., Extended dissipative state estimation for memristive neural networks with time-varying delay, ISA Trans., 64, 113-128 (2016) |
| [71] | Selvaraj, P.; Sakthivel, R.; Kwon, O. M., Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation, Neural Netw., 105, 154-165 (2018) · Zbl 1441.93327 |
| [72] | Ali, M. S.; Vadivel, R.; Saravanakumar, R., Design of robust reliable control for T-S fuzzy Markovian jumping delayed neutral type neural networks with probabilistic actuator faults and leakage delays: an event-triggered communication scheme, ISA Trans., 77, 30-48 (2018) |
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.
