Document Zbl 1357.93096

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C.</a>; <a href="/authors/wei.guoliang" title="Author Profile">Wei, Guoliang</a></div> <h2 class="title"> <strong>Distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks.</strong> <i>(English)</i> <a class="label nowrap" href="/1357.93096">Zbl 1357.93096</a> </h2> <div class="source"> <a href="/serials/348" title="Journal Profile">Automatica</a> <a href="/?q=in%3A364435" title="Articles in this Issue">78, 231-240 (2017)</a>. </div> <div class="abstract">Summary: This paper is concerned with the distributed recursive filtering problem for a class of discrete time-delayed stochastic systems subject to both uniform quantization and deception attack effects on the measurement outputs. The target plant is disturbed by the multiplicative as well as additive white noises. A novel distributed filter is designed where the available innovations are from not only the individual sensor but also its neighboring ones according to the given topology. Attention is focused on the design of a distributed recursive filter such that, in the simultaneous presence of time-delays, deception attacks and uniform quantization effects, an upper bound for the filtering error covariance is guaranteed and subsequently minimized by properly designing the filter parameters via a gradient-based method at each sampling instant. Furthermore, by utilizing the mathematical induction, a sufficient condition is established to ensure the asymptotic boundedness of the sequence of the error covariance. Finally, a simulation example is utilized to illustrate the usefulness of the proposed design scheme of distributed filters.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6697704">Cited in <strong>110</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A93E10" title="MSC2020">93E10</a> </td> <td class="space"> Estimation and detection in stochastic control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C55" title="MSC2020">93C55</a> </td> <td class="space"> Discrete-time control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E03" title="MSC2020">93E03</a> </td> <td class="space"> Stochastic systems in control theory (general) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asensor+networks">sensor networks</a>; <a href="/?q=ut%3Adistributed+filtering">distributed filtering</a>; <a href="/?q=ut%3Arecursive+filtering">recursive filtering</a>; <a href="/?q=ut%3Adeception+attacks">deception attacks</a>; <a href="/?q=ut%3Auniform+quantization">uniform quantization</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 1357.93096" data-ciurl="/ci/06697704" data-biburl="/bibtex/06697704.bib" data-amsurl="/amsrefs/06697704.bib" data-xmlurl="/xml/06697704.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06697704.pdf" title="Zbl 1357.93096 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.automatica.2016.12.026" aria-label="DOI for “Distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks”" title="10.1016/j.automatica.2016.12.026">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://bura.brunel.ac.uk/handle/2438/14341" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Amin, S.; Schwartz, G. A.; Shankar Sastry, S., Security of interdependent and identical networked control systems, Automatica, 49, 1, 186-192 (2013) · <a href="/1257.93012" class="nowrap">Zbl 1257.93012</a></td> </tr><tr> <td>[2]</td> <td class="space">Basin, M.; Alcorta-Garcia, A.; Rodriguez-Gonzalez, J., Optimal filtering for linear systems with state and observation delays, International Journal of Robust and Nonlinear Control, 15, 17, 859-871 (2005) · <a href="/1086.93058" class="nowrap">Zbl 1086.93058</a></td> </tr><tr> <td>[3]</td> <td class="space">Basin, M.; Martinez-Zuniga, R., Optimal linear filtering over observations with multiple delays, International Journal of Robust and Nonlinear Control, 14, 8, 685-696 (2004) · <a href="/1057.93055" class="nowrap">Zbl 1057.93055</a></td> </tr><tr> <td>[4]</td> <td class="space">Brockett, R. W.; Liberzon, D., Quantized feedback stabilization of linear systems, IEEE Transactions on Automatic Control, 55, 7, 1279-1289 (2000) · <a href="/0988.93069" class="nowrap">Zbl 0988.93069</a></td> </tr><tr> <td>[5]</td> <td class="space">Chen, H.; Liang, J.; Wang, Z., Pinning controllability of autonomous Boolean control networks, Science China Information Sciences, 59, 7 (2016), Art. No. 070107</td> </tr><tr> <td>[6]</td> <td class="space">Ding, D.; Wang, Z.; Ho, D. W.C.; Wei, G., Observer-based event-triggering consensus control for multi-agent systems with lossy sensors and cyber attacks, IEEE Transactions on Cybernetics (2016)</td> </tr><tr> <td>[7]</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>[8]</td> <td class="space">Dong, H.; Wang, Z.; Alsaadi, F. E.; Ahmad, B., Event-triggered robust distributed state estimation for sensor networks with state-dependent noises, International Journal of General Systems, 44, 2, 254-266 (2015) · <a href="/1309.93100" class="nowrap">Zbl 1309.93100</a></td> </tr><tr> <td>[9]</td> <td class="space">Dong, H.; Wang, Z.; Gao, H., Distributed $H_\infty$ filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks, IEEE Transactions on Industrial Electronics, 60, 10, 4665-4672 (2013)</td> </tr><tr> <td>[10]</td> <td class="space">Dong, H.; Wang, Z.; Shen, B.; Ding, D., Variance-constrained $H_\infty$ control for a class of nonlinear stochastic discrete time-varying systems: the event-triggered design, Automatica, 72, 28-36 (2016) · <a href="/1344.93089" class="nowrap">Zbl 1344.93089</a></td> </tr><tr> <td>[11]</td> <td class="space">Fawzi, H.; Tabuada, P.; Diggavi, S., Secure estimation and control for cyber-physical systems under adversarial attacks, IEEE Transactions on Automatic Control, 59, 6, 1454-1467 (2014) · <a href="/1360.93201" class="nowrap">Zbl 1360.93201</a></td> </tr><tr> <td>[12]</td> <td class="space">Gandhi, M. A.; Mili, L., Robust Kalman filter based on a generalized maximum-likelihood-type estimator, IEEE Transactions on Automatic Control, 58, 5, 2509-2520 (2010) · <a href="/1392.94216" class="nowrap">Zbl 1392.94216</a></td> </tr><tr> <td>[13]</td> <td class="space">Gershon, E.; Shaked, U.; Yaesh, I., $H_\infty$ control and filtering of discrete-time stochastic systems with multiplicative noise, Automatica, 37, 3, 409-417 (2001) · <a href="/0989.93030" class="nowrap">Zbl 0989.93030</a></td> </tr><tr> <td>[14]</td> <td class="space">Hou, N.; Dong, H.; Wang, Z.; Ren, W.; Alsaadi, F. E., Non-fragile state estimation for discrete Markovian jumping neural networks, Neurocomputing, 179, 238-245 (2016)</td> </tr><tr> <td>[15]</td> <td class="space">Hu, J.; Chen, D.; Du, J., State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays, International Journal of General Systems, 43, 3-4, 387-401 (2014) · <a href="/1302.93201" class="nowrap">Zbl 1302.93201</a></td> </tr><tr> <td>[16]</td> <td class="space">Hu, J.; Liu, S.; Ji, D.; Li, S., On co-design of filter and fault estimator against randomly occurring nonlinearities and randomly occurring deception attacks, International Journal of General Systems, 45, 5, 619-632 (2016) · <a href="/1342.93112" class="nowrap">Zbl 1342.93112</a></td> </tr><tr> <td>[17]</td> <td class="space">Kluge, S.; Reif, K.; Brokate, M., Stochastic stability of the extended Kalman filter with intermittent observations, IEEE Transactions on Automatic Control, 55, 2, 514-518 (2010) · <a href="/1368.93717" class="nowrap">Zbl 1368.93717</a></td> </tr><tr> <td>[18]</td> <td class="space">Kong, S.; Saif, M.; Zhang, H., Optimal filtering for-stochastic continuous-time systems with multiple delayed measurements, IEEE Transactions on Automatic Control, 58, 7, 1872-1877 (2013) · <a href="/1369.93634" class="nowrap">Zbl 1369.93634</a></td> </tr><tr> <td>[19]</td> <td class="space">Li, Q.; Shen, B.; Liang, J.; Shu, H., Event-triggered synchronization control for complex networks with uncertain inner coupling, International Journal of General Systems, 44, 2, 212-225 (2015) · <a href="/1309.93101" class="nowrap">Zbl 1309.93101</a></td> </tr><tr> <td>[20]</td> <td class="space">Li, Q.; Shen, B.; Liu, Y.; Alsaadi, F. E., Event-triggered $H_\infty$ state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays, Neurocomputing, 174, 912-920 (2016)</td> </tr><tr> <td>[21]</td> <td class="space">Long, M.; Wu, C.-H.; Hung, J. Y., Denial of service attacks on network-based control systems: impact and mitigation, IEEE Transactions on Industrial Informatics, 1, 2, 85-96 (2005)</td> </tr><tr> <td>[22]</td> <td class="space">Lu, L.-Z., Some new bounds for singular values and eigenvalues of matrix products, Annals of Operations Research, 98, 1-4, 141-148 (2000) · <a href="/0979.15017" class="nowrap">Zbl 0979.15017</a></td> </tr><tr> <td>[23]</td> <td class="space">Lu, X.; Xie, L.; Zhang, H.; Wang, W., Robust Kalman filtering for discrete-time systems with measurement delay, IEEE Transactions on Circuits and Systems-II, 54, 6, 522-526 (2007)</td> </tr><tr> <td>[24]</td> <td class="space">Marano, S.; Matta, V.; Tong, L., Distributed detection in the presence of Byzantine attacks, IEEE Transactions on Signal Processing, 57, 1, 16-29 (2009) · <a href="/1391.94534" class="nowrap">Zbl 1391.94534</a></td> </tr><tr> <td>[26]</td> <td class="space">Pang, Z.-H.; Liu, G.-P., Design and implementation of secure networked predictive control systems under deception attacks, IEEE Transactions on Control Systems Technology, 20, 5, 1334-1342 (2012)</td> </tr><tr> <td>[27]</td> <td class="space">Reif, K.; Günther, S.; Yaz, E.; Unbehauen, R., Stochastic stability of the discrete-time extended Kalman filter, IEEE Transactions on Automatic Control, 44, 4, 714-728 (1999) · <a href="/0967.93090" class="nowrap">Zbl 0967.93090</a></td> </tr><tr> <td>[28]</td> <td class="space">Rojas, A. J.; Lotero, F., Signal-to-noise ratio limited output feedback control subject to channel input quantization, IEEE Transactions on Automatic Control, 60, 2, 475-479 (2015) · <a href="/1360.93266" class="nowrap">Zbl 1360.93266</a></td> </tr><tr> <td>[29]</td> <td class="space">Simon, D.; Chia, T., Kalman filtering with state equality constraints, IEEE Transactions on Aerospace and Electronic Systems, 38, 1, 128-136 (2002)</td> </tr><tr> <td>[30]</td> <td class="space">Theodor, Y.; Shaked, U., Robust discrete-time minimum-variance filtering, IEEE Transactions on Signal Processing, 44, 2, 181-189 (1996)</td> </tr><tr> <td>[31]</td> <td class="space">Vempaty, A.; Ozdemir, O.; Agrawal, K.; Chen, H.; Varshney, P. K., Localization in wireless sensor networks: Byzantines and mitigation techniques, IEEE Transactions on Signal Processing, 61, 6, 1495-1508 (2013) · <a href="/1393.90043" class="nowrap">Zbl 1393.90043</a></td> </tr><tr> <td>[32]</td> <td class="space">Vempaty, A.; Tong, L.; Varshney, P., Distributed inference with Byzantine data: State-of-the-art review on data falsification attacks, IEEE Signal Processing Magazine, 30, 5, 65-75 (2013)</td> </tr><tr> <td>[33]</td> <td class="space">Yang, F.; Dong, H.; Wang, Z.; Ren, W.; Alsaadi, F. E., A new approach to non-fragile state estimation for continuous neural networks with time-delays, Neurocomputing, 197, 205-211 (2016)</td> </tr><tr> <td>[34]</td> <td class="space">Yang, H.; Wang, Z.; Shu, H.; Alsaadi, F. E.; Hayat, T., Almost sure $H_\infty$ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays, Neurocomputing, 175, 392-400 (2016)</td> </tr><tr> <td>[35]</td> <td class="space">Yu, Y.; Dong, H.; Wang, Z.; Ren, W.; Alsaadi, F. E., Design of non-fragile state estimators for discrete time-delayed neural networks with parameter uncertainties, Neurocomputing, 182, 18-24 (2016)</td> </tr><tr> <td>[36]</td> <td class="space">Zeng, N.; Wang, Z.; Zhang, H., Inferring nonlinear lateral flow immunoassay state-space models via an unscented Kalman filter, Science China Information Sciences, 59, 11 (2016), Art. No. 112204</td> </tr><tr> <td>[37]</td> <td class="space">Zhang, J.; Blum, R. S.; Lu, X.; Conus, D., Asymptotically optimum distributed estimation in the presence of attacks, IEEE Transactions on Signal Processing, 63, 5, 1086-1101 (2015) · <a href="/1394.94684" class="nowrap">Zbl 1394.94684</a></td> </tr><tr> <td>[38]</td> <td class="space">Zhu, M.; Martinez, S., On the performance analysis of resilient networked control systems under replay attacks, IEEE Transactions on Automatic Control, 59, 3 (2014) · <a href="/1360.93459" class="nowrap">Zbl 1360.93459</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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