Document Zbl 1426.93086

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Math. Comput.</a> <a href="/?q=in%3A434399" title="Articles in this Issue">320, 158-174 (2018)</a>. </div> <div class="abstract">Summary: This paper investigates the problem of $H_{\infty}$ filter design for neural networks with hybrid triggered scheme and deception attacks. In order to make full use of the limited network resources, a hybrid triggered scheme is introduced, in which the switching between the time triggered scheme and the event triggered scheme obeys Bernoulli distribution. By considering the effect of hybrid triggered scheme and deception attacks, a mathematical model of $H_{\infty}$ filtering error system is constructed. The sufficient conditions that can ensure the stability of filtering error system are given by using Lyapunov stability theory and linear matrix inequality (LMI) techniques. Moreover, the explicit expressions are provided for the designed filter parameters that is in terms of LMIs. Finally, a numerical example is employed to illustrate the design method.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7070016">Cited in <strong>53</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B36" title="MSC2020">93B36</a> </td> <td class="space"> $H^\infty$-control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K20" title="MSC2020">34K20</a> </td> <td class="space"> Stability theory of functional-differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E11" title="MSC2020">93E11</a> </td> <td class="space"> Filtering in stochastic control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92B20" title="MSC2020">92B20</a> </td> <td class="space"> Neural networks for/in biological studies, artificial life and related topics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aneural+networks">neural networks</a>; <a href="/?q=ut%3Ahybrid+triggered+scheme">hybrid triggered scheme</a>; <a href="/?q=ut%3A%5C%28H_%7B%5Cinfty%7D%5C%29+filter+design">$H_{\infty}$ filter design</a>; <a href="/?q=ut%3Adeception+attacks">deception attacks</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1426.93086" data-ciurl="/ci/07070016" data-biburl="/bibtex/07070016.bib" data-amsurl="/amsrefs/07070016.bib" data-xmlurl="/xml/07070016.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07070016.pdf" title="Zbl 1426.93086 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.amc.2017.09.007" aria-label="DOI for “Hybrid-driven-based $H_{\infty}$ filter design for neural networks subject to deception attacks”" title="10.1016/j.amc.2017.09.007">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Park, J. H., A new stability analysis of delayed cellular neural networks, Appl. Math. Comput., 181, 1, 200-205 (2006) · <a href="/1154.34386" class="nowrap">Zbl 1154.34386</a></td> </tr><tr> <td>[2]</td> <td class="space">Ju, H. P., Further result on asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays, Appl. Math. Comput., 182, 2, 1661-1666 (2006) · <a href="/1154.92302" class="nowrap">Zbl 1154.92302</a></td> </tr><tr> <td>[3]</td> <td class="space">Ju, H. P.; Park, C. H.; Kwon, O. M.; Lee, S. M., A new stability criterion for bidirectional associative memory neural networks of neutral-type, Appl. Math. Comput., 199, 2, 716-722 (2008) · <a href="/1149.34345" class="nowrap">Zbl 1149.34345</a></td> </tr><tr> <td>[4]</td> <td class="space">Wei, Y.; Park, J. H.; Karimi, H. R.; Tian, Y. C.; Jung, H., Improved stability and stabilization results for stochastic synchronization of continuous-time semi-Markovian jump neural networks with time-varying delay, IEEE Trans. Neural Netw. Learn. Syst., 99, 1-14 (2017)</td> </tr><tr> <td>[5]</td> <td class="space">Liu, Y.; Lee, S. M.; Lee, H. G., Robust delay-depent stability criteria for uncertain neural networks with two additive time-varying delay components, Neurocomputing, 151, 151, 770-775 (2015)</td> </tr><tr> <td>[6]</td> <td class="space">Ali, M. S.; Saravanakumar, R.; Ahn, C. K.; Karimi, H. R., Stochastic $h_∞$ filtering for neural networks with leakage delay and mixed time-varying delays, Inf. Sci., 388-389, 118-134 (2017) · <a href="/1432.93356" class="nowrap">Zbl 1432.93356</a></td> </tr><tr> <td>[7]</td> <td class="space">Chen, M.; Zhang, L.; Shen, H., Resilient $h_∞$ filtering for discrete-time uncertain Markov jump neural networks over a finite-time interval, Neurocomputing, 185, 212-219 (2016)</td> </tr><tr> <td>[8]</td> <td class="space">Park, J. H.; Kwon, O.; Lee, S.; Won, S., On robust $h_∞$ filter design for uncertain neural systems: LMI optimization approach, Appl. Math. Comput., 159, 3, 625-639 (2004) · <a href="/1061.93092" class="nowrap">Zbl 1061.93092</a></td> </tr><tr> <td>[9]</td> <td class="space">Liu, J.; Tang, J.; Fei, S., Event-triggered $h_∞$ filter design for delayed neural network with quantization, Neural Netw., 82, 39-48 (2016) · <a href="/1429.93384" class="nowrap">Zbl 1429.93384</a></td> </tr><tr> <td>[10]</td> <td class="space">Wei, J. Q.L. W.H. Y.J. Y.; Park, J. H., Sliding mode control for semi-Markovian jump systems via output feedback, Aumatica, 81, 133-141 (2017) · <a href="/1376.93029" class="nowrap">Zbl 1376.93029</a></td> </tr><tr> <td>[11]</td> <td class="space">Yue, D.; Han, Q. L.; Lam, J., Network-based robust protect $h_∞$ control of systems with uncertainty, Automatica, 41, 6, 999-1007 (2005) · <a href="/1091.93007" class="nowrap">Zbl 1091.93007</a></td> </tr><tr> <td>[12]</td> <td class="space">Dong, Y.; Tian, E.; Han, Q. L., A delay system method for designing event-triggered controllers of networked control systems, IEEE Trans. Autom. Control, 58, 2, 475-481 (2013) · <a href="/1369.93183" class="nowrap">Zbl 1369.93183</a></td> </tr><tr> <td>[13]</td> <td class="space">Liu, J.; Wu, F.; Zha, L.; Fei, S., Co-design of event generator and state estimator for complex network systems with quantization, J. Frankl. Inst., 353, 17, 4565-4582 (2016) · <a href="/1349.93366" class="nowrap">Zbl 1349.93366</a></td> </tr><tr> <td>[14]</td> <td class="space">Peng, C.; Tian, E.; Zhang, J.; Du, D., Decentralized event-triggering communication scheme for large-scale systems under network environments, Inf. Sci., 380, 132-144 (2015)</td> </tr><tr> <td>[15]</td> <td class="space">Zhang, C.; Hu, J.; Qiu, J.; Chen, Q., Event-triggered nonsynchronized $h_∞$ filtering for discrete-time t-s fuzzy systems based on piecewise Lyapunov functions, IEEE Trans. Syst. Man Cybern. Syst., 47, 8, 2330-2341 (2017)</td> </tr><tr> <td>[16]</td> <td class="space">Hu, S.; Dong, Y., Event-triggered control design of linear networked systems with quantizations, ISA Trans., 51, 1, 153-162 (2012)</td> </tr><tr> <td>[17]</td> <td class="space">Liu, J.; Zha, L.; Cao, J.; Fei, S., Hybrid-driven-based stabilisation for networked control systems, IET Control Theory Appl., 10, 17, 2279-2285 (2016)</td> </tr><tr> <td>[18]</td> <td class="space">Zha, L.; Fang, J. A.; Liu, J.; Tian, E., Reliable control for hybrid-driven t-s fuzzy systems with actuator faults and probabilistic nonlinear perturbations, J. Frankl. Inst., 354, 8, 3267-3288 (2017) · <a href="/1364.93425" class="nowrap">Zbl 1364.93425</a></td> </tr><tr> <td>[19]</td> <td class="space">Ding, D.; Wei, G.; Zhang, S.; Liu, Y.; Alsaadi, F. E., On scheduling of deception attacks for discrete-time networked systems equipped with attack detectors, Neurocomputing, 219, 99-106 (2017)</td> </tr><tr> <td>[20]</td> <td class="space">Ding, D.; Wang, Z.; Ho, D. W.C.; Wei, G., Distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks, Automatica, 78, 231-240 (2017) · <a href="/1357.93096" class="nowrap">Zbl 1357.93096</a></td> </tr><tr> <td>[21]</td> <td class="space">W. Yang, L. Lei, C. Yang, Event-based distributed state estimation under deception attack, Neurocomputing. https://doi.org/10.1016/j.neucom.2016.12.109; W. Yang, L. Lei, C. Yang, Event-based distributed state estimation under deception attack, Neurocomputing. https://doi.org/10.1016/j.neucom.2016.12.109</td> </tr><tr> <td>[22]</td> <td class="space">Xie, X.; Yue, D.; Ma, T.; Zhu, X., Further studies on control synthesis of discrete-time t-s fuzzy systems via augmented multi-indexed matrix approach, IEEE Trans. Cybern., 44, 12, 2784-2791 (2014)</td> </tr><tr> <td>[23]</td> <td class="space">Tian, E.; Yue, D.; Peng, C., Brief paper: reliable control for networked control systems with probabilistic sensors and actuators faults, Control Theory Appl. IET, 4, 8, 1478-1488 (2010)</td> </tr><tr> <td>[24]</td> <td class="space">Liu, Y.; Guo, B. Z.; Ju, H. P.; Lee, S. M., Nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control, IEEE Trans. Neural Netw. Learn. Syst., 99, 1-11 (2016)</td> </tr><tr> <td>[25]</td> <td class="space">Liu, J.; Fei, S.; Tian, E.; Gu, Z., Co-design of event generator and filtering for a class of t-s fuzzy systems with stochastic sensor faults, Fuzzy Sets Syst., 273, 124-140 (2015) · <a href="/1373.93347" class="nowrap">Zbl 1373.93347</a></td> </tr><tr> <td>[26]</td> <td class="space">Peng, C.; Yang, T. C., Event-triggered communication and $h_∞$ mathcontainer loading mathjax control co-design for networked control systems, Automatica, 49, 5, 1326-1332 (2013) · <a href="/1319.93022" class="nowrap">Zbl 1319.93022</a></td> </tr><tr> <td>[27]</td> <td class="space">Lin, X.; Li, X.; Li, S.; Zou, Y., Finite-time boundedness for switched systems with sector bounded nonlinearity and constant time delay, Appl. Math. Comput., 274, 25-40 (2016) · <a href="/1410.93107" class="nowrap">Zbl 1410.93107</a></td> </tr><tr> <td>[28]</td> <td class="space">Tian, E.; Yue, D., Decentralized control of network-based interconnected systems: a state-dependent triggering method, Int. J. Robust Nonlinear Control, 25, 8, 1126-1144 (2013) · <a href="/1317.93021" class="nowrap">Zbl 1317.93021</a></td> </tr><tr> <td>[29]</td> <td class="space">Wang, Z.; Yang, F.; Ho, D. W.C.; Liu, X., Robust filtering for stochastic time-delay systems with missing measurements, IEEE Trans. Signal Process., 54, 7, 2579-2587 (2006) · <a href="/1373.94729" class="nowrap">Zbl 1373.94729</a></td> </tr><tr> <td>[30]</td> <td class="space">Zhang, J.; Wang, Z.; Ding, D.; Liu, X., $h_∞$ state estimation for discrete-time delayed neural networks with randomly occurring quantizations and missing measurements, Neurocomputing, 148, 388-396 (2015)</td> </tr><tr> <td>[31]</td> <td class="space">Mao, X., Exponential stability of stochastic delay interval systems with Markovian switching, Syst. Control Lett., 47, 10, 1604-1612 (2000) · <a href="/1364.93685" class="nowrap">Zbl 1364.93685</a></td> </tr><tr> <td>[32]</td> <td class="space">Li, N.; Hu, J.; Hu, J.; Li, L., Exponential state estimation for delayed recurrent neural networks with sampled-data, Nonlinear Dyn., 69, 69, 555-564 (2012) · <a href="/1253.93082" class="nowrap">Zbl 1253.93082</a></td> </tr><tr> <td>[33]</td> <td class="space">Gu, K.; Kharitonov, V. L.; Chen, J., Introduction to time-delay systems, Syst. Control Found. Appl., 72, 4, 591-597 (2003)</td> </tr><tr> <td>[34]</td> <td class="space">Li, H.; Sun, X.; Shi, P.; Lam, H. K., Control design of interval type-2 fuzzy systems with actuator fault: sampled-data control approach, Inf. Sci., 302, 1-13 (2015) · <a href="/1360.93377" class="nowrap">Zbl 1360.93377</a></td> </tr><tr> <td>[35]</td> <td class="space">Wang, Y.; Xie, L.; Souza, C. E.D., Robust control of a class of uncertain nonlinear systems, Syst. Control Lett., 19, 2, 139-149 (1997) · <a href="/0765.93015" class="nowrap">Zbl 0765.93015</a></td> </tr><tr> <td>[36]</td> <td class="space">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. Part B Cybern., 39, 2, 503-516 (2009)</td> </tr><tr> <td>[37]</td> <td class="space">He, Y.; Wu, M.; She, J. H.; Liu, G. P., Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties, IEEE Trans. Autom. Control, 49, 5, 828-832 (2004) · <a href="/1365.93368" class="nowrap">Zbl 1365.93368</a></td> </tr></table> <div class="reference_disclaimer"> 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. 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