Document Zbl 1193.93160

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Math. Appl.</a> <a href="/?q=in%3A261200" title="Articles in this Issue">59, No. 8, 2636-2646 (2010)</a>. </div> <div class="abstract">Summary: This paper addresses a decentralized robust set-valued state estimation problem for a class of uncertain systems via a data-rate constrained sensor network. The uncertainties of the systems satisfy an energy-type constraint known as an integral quadratic constraint. The sensor network consists of spatially distributed sensors and a fusion center where set-valued state estimation is carried out. The communications from the sensors to the fusion center are through data-rate constrained communication channels. We propose a state estimation scheme which involves coders that are implemented in the sensors, and a decoder-estimator that is located at the fusion center. Their construction is based on the robust Kalman filtering techniques. The robust set-valued state estimation results of this paper involve the solution of a jump Riccati differential equation and the solution of a set of jump state equations.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5775029">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%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%3A93C57" title="MSC2020">93C57</a> </td> <td class="space"> Sampled-data control/observation systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Arobust+control">robust control</a>; <a href="/?q=ut%3Anetworked+control+systems">networked control systems</a>; <a href="/?q=ut%3Astate+estimation+under+uncertainty">state estimation under uncertainty</a>; <a href="/?q=ut%3Asensor+fusion">sensor fusion</a>; <a href="/?q=ut%3Adecentralized+estimation">decentralized estimation</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 1193.93160" data-ciurl="/ci/05775029" data-biburl="/bibtex/05775029.bib" data-amsurl="/amsrefs/05775029.bib" data-xmlurl="/xml/05775029.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05775029.pdf" title="Zbl 1193.93160 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.camwa.2010.01.032" aria-label="DOI for “Decentralized robust set-valued state estimation in networked multiple sensor systems”" title="10.1016/j.camwa.2010.01.032">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">Murphy, R. R., Sensor and information fusion for improved vision-based vehicle guidance, IEEE Intelligent Systems, 13, 6, 49-56 (1998)</td> </tr><tr> <td>[2]</td> <td class="space">Pathirana, P. N.; Lim, A. E.K.; Savkin, A. V.; Hodgson, P. D., Robust video/ultrasonic fusion-based estimation for automotive applications, IEEE Transactions on Vehicular Technology, 56, 4, 1631-1639 (2007)</td> </tr><tr> <td>[3]</td> <td class="space">Savkin, A. V.; Petersen, I. R., Set-valued state estimation via a limited capacity communication channel, IEEE Transactions on Automatic Control, 48, 4, 676-680 (2003) · <a href="/1364.93784" class="nowrap">Zbl 1364.93784</a></td> </tr><tr> <td>[4]</td> <td class="space">Matveev, A., State estimation via limited capacity noisy communication channels, Mathematics of Control, Signals, and Systems, 20, 1, 1-35 (2008) · <a href="/1144.93019" class="nowrap">Zbl 1144.93019</a></td> </tr><tr> <td>[5]</td> <td class="space">Matveev, A. S.; Savkin, A. V., The problem of state estimation via asynchronous communication channels with irregular transmission times, IEEE Transactions on Automatic Control, 48, 4, 670-676 (2003) · <a href="/1364.93779" class="nowrap">Zbl 1364.93779</a></td> </tr><tr> <td>[6]</td> <td class="space">Malyavej, V.; Savkin, A. V., The problem of optimal robust Kalman state estimation via limited capacity digital communication channels, Systems & Control Letters, 54, 283-292 (2005) · <a href="/1129.93539" class="nowrap">Zbl 1129.93539</a></td> </tr><tr> <td>[7]</td> <td class="space">Gao, H.; Chen, T., $H_\infty$ estimation for uncertain systems with limited communication capacity, IEEE Transactions on Automatic Control, 52, 11, 2070-2084 (2007) · <a href="/1366.93155" class="nowrap">Zbl 1366.93155</a></td> </tr><tr> <td>[8]</td> <td class="space">Linares-Pérez, J.; Hermoso-Carazo, A.; Caballero-Águila, R.; Jiménez-López, J., Least-squares linear filtering using observations coming from multiple sensors with one- or two-step random delay, Signal Processing, 89, 10, 2045-2052 (2009) · <a href="/1178.94142" class="nowrap">Zbl 1178.94142</a></td> </tr><tr> <td>[9]</td> <td class="space">Suh, Y.; Nguyen, V.; Ro, Y., Modified Kalman filter for networked monitoring systems employing a send-on-delta method, Automatica, 43, 2, 332-338 (2007) · <a href="/1111.93080" class="nowrap">Zbl 1111.93080</a></td> </tr><tr> <td>[10]</td> <td class="space">Sun, S., Linear minimum variance estimators for systems with bounded random measurement delays and packet dropouts, Signal Processing, 89, 7, 1457-1466 (2009) · <a href="/1178.94153" class="nowrap">Zbl 1178.94153</a></td> </tr><tr> <td>[11]</td> <td class="space">Song, H.; Yu, L.; Zhang, W.-A., $H_\infty$ filtering of network-based systems with random delay, Signal Processing, 89, 4, 615-622 (2009) · <a href="/1157.93529" class="nowrap">Zbl 1157.93529</a></td> </tr><tr> <td>[12]</td> <td class="space">Han, C.; Zhang, H., Linear optimal filtering for discrete-time systems with random jump delays, Signal Processing, 89, 6, 1121-1128 (2009) · <a href="/1161.94332" class="nowrap">Zbl 1161.94332</a></td> </tr><tr> <td>[13]</td> <td class="space">Caballero-Águila, R.; Hermoso-Carazo, A.; Jiménez-López, J.; Linares-Pŕez, J.; Nakamori, S., Recursive estimation of discrete-time signals from nonlinear randomly delayed observations, Computers and Mathematics with Applications, 58, 6, 1160-1168 (2009) · <a href="/1189.93136" class="nowrap">Zbl 1189.93136</a></td> </tr><tr> <td>[14]</td> <td class="space">R. Caballero-Águila, A. Hermoso-Carazo, J. Jiménez-López, J. Linares-Pŕez, S. Nakamori, Signal estimation with multiple delayed sensors using covariance information, Digital Signal Processing: A Review Journal, 2009, in press (doi:10.1016/j.dsp.2009.06.011; R. Caballero-Águila, A. Hermoso-Carazo, J. Jiménez-López, J. Linares-Pŕez, S. Nakamori, Signal estimation with multiple delayed sensors using covariance information, Digital Signal Processing: A Review Journal, 2009, in press (doi:10.1016/j.dsp.2009.06.011</td> </tr><tr> <td>[15]</td> <td class="space">M. Fu, C.E. de Souza, State estimation using quantized measurements, in: Proceedings of the 17th IFAC World Congress, Seoul, South Korea, 2008, pp. 12492-12497.; M. Fu, C.E. de Souza, State estimation using quantized measurements, in: Proceedings of the 17th IFAC World Congress, Seoul, South Korea, 2008, pp. 12492-12497.</td> </tr><tr> <td>[16]</td> <td class="space">Charalambous, C. D.; Farhadi, A., LQG optimality and separation principle for general discrete time partially observed stochastic systems over finite capacity communication channels, Automatica, 44, 12, 3181-3188 (2008) · <a href="/1153.93530" class="nowrap">Zbl 1153.93530</a></td> </tr><tr> <td>[17]</td> <td class="space">Zhang, Y.; Tang, G.-Y.; Hu, N.-P., Non-fragile control for nonlinear networked control systems with long time-delay, Computers and Mathematics with Applications, 57, 10, 1630-1637 (2009) · <a href="/1186.93031" class="nowrap">Zbl 1186.93031</a></td> </tr><tr> <td>[18]</td> <td class="space">Zhou, L.; Lu, G., Detection and stabilization for discrete-time descriptor systems via a limited capacity communication channel, Automatica, 45, 10, 2272-2277 (2009) · <a href="/1179.93153" class="nowrap">Zbl 1179.93153</a></td> </tr><tr> <td>[19]</td> <td class="space">I.R. Petersen, A.V. Savkin, Multi-rate stabilization of multivariable discrete-time linear systems via a limited capacity communication channel, in: Proc. 40th IEEE Conf. Decision and Control, Orlando, Florida, USA, 2001, pp. 304-309.; I.R. Petersen, A.V. Savkin, Multi-rate stabilization of multivariable discrete-time linear systems via a limited capacity communication channel, in: Proc. 40th IEEE Conf. Decision and Control, Orlando, Florida, USA, 2001, pp. 304-309.</td> </tr><tr> <td>[20]</td> <td class="space">Matveev, A. S.; Savkin, A. V., Multi-rate stabilization of linear multiple sensor systems via limited capacity communication channels, SIAM Journal on Control and Optimization, 44, 2, 584-617 (2005) · <a href="/1130.93405" class="nowrap">Zbl 1130.93405</a></td> </tr><tr> <td>[21]</td> <td class="space">Savkin, A. V., Analysis and synthesis of networked control systems: Topological entropy, observability, robustness, and optimal control, Automatica, 42, 1, 51-62 (2006) · <a href="/1121.93321" class="nowrap">Zbl 1121.93321</a></td> </tr><tr> <td>[22]</td> <td class="space">Savkin, A. V.; Cheng, T. M., Detectability and output feedback stabilizability of nonlinear networked control systems, IEEE Transactions on Automatic Control, 52, 4, 730-735 (2007) · <a href="/1366.93526" class="nowrap">Zbl 1366.93526</a></td> </tr><tr> <td>[23]</td> <td class="space">Cheng, T. M.; Savkin, A. V., Output feedback stabilisation of nonlinear networked control systems with non-decreasing nonlinearities: A matrix inequalities approach, International Journal of Robust and Nonlinear Control, 17, 5, 387-404 (2007) · <a href="/1113.93085" class="nowrap">Zbl 1113.93085</a></td> </tr><tr> <td>[24]</td> <td class="space">Matveev, A. S.; Savkin, A. V., An analogue of Shannon information theory for detection and stabilization of via noisy discrete communication channels, SIAM Journal on Control and Optimization, 46, 4, 1323-1367 (2007) · <a href="/1140.93016" class="nowrap">Zbl 1140.93016</a></td> </tr><tr> <td>[25]</td> <td class="space">Matveev, A. S.; Savkin, A. V., Estimation and Control over Communication Networks (2009), Birkhäuser: Birkhäuser Boston · <a href="/1165.93003" class="nowrap">Zbl 1165.93003</a></td> </tr><tr> <td>[26]</td> <td class="space">Savkin, A. V.; Petersen, I. R., Recursive state estimation for uncertain systems with an integral quadratic constraint, IEEE Transactions on Automatic Control, 40, 6, 1080-1083 (1995) · <a href="/0829.93060" class="nowrap">Zbl 0829.93060</a></td> </tr><tr> <td>[27]</td> <td class="space">Bertsekas, D. P.; Rhodes, I., Recursive state estimation for a set-membership description of uncertainty, IEEE Transactions on Automatic Control, AC-16, 2, 117-128 (1971)</td> </tr><tr> <td>[28]</td> <td class="space">Petersen, I. R.; Ugrinovskii, V. A.; Savkin, A. V., Robust Control Design Using $H^\infty$ Methods (2000), Springer-Verlag: Springer-Verlag London · <a href="/0963.93003" class="nowrap">Zbl 0963.93003</a></td> </tr><tr> <td>[29]</td> <td class="space">Petersen, I. R.; Savkin, A. V., Robust Kalman Filtering for Signals and Systems with Large Uncertainties (1999), Birkhäuser: Birkhäuser Boston · <a href="/1033.93002" class="nowrap">Zbl 1033.93002</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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