<doi_batch xmlns="http://www.crossref.org/schema/4.4.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" version="4.4.0"><head><doi_batch_id>2a8200e6-4601-43f9-947c-2ef5cc3ec2b7</doi_batch_id><timestamp>20240329052352979</timestamp><depositor><depositor_name>wseas:wseas</depositor_name><email_address>mdt@crossref.org</email_address></depositor><registrant>MDT Deposit</registrant></head><body><journal><journal_metadata language="en"><full_title>WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL</full_title><issn media_type="electronic">2224-2856</issn><issn media_type="print">1991-8763</issn><archive_locations><archive name="Portico"/></archive_locations><doi_data><doi>10.37394/23203</doi><resource>http://wseas.org/wseas/cms.action?id=4073</resource></doi_data></journal_metadata><journal_issue><publication_date media_type="online"><month>1</month><day>2</day><year>2023</year></publication_date><publication_date media_type="print"><month>1</month><day>2</day><year>2023</year></publication_date><journal_volume><volume>18</volume><doi_data><doi>10.37394/23203.2023.18</doi><resource>https://wseas.com/journals/sac/2023.php</resource></doi_data></journal_volume></journal_issue><journal_article language="en"><titles><title>Sentinels for the Identification of Pollution in Domains with Missing Data</title></titles><contributors><person_name sequence="first" contributor_role="author"><given_name>Rezzoug</given_name><surname>Imad</surname><affiliation>Department of Mathematics and Computer Science,  University of Oum El Bouaghi,  Laboratory of Dynamics systems and control,  ALGERIA</affiliation></person_name><person_name sequence="additional" contributor_role="author"><given_name>Achab</given_name><surname>Fatma</surname><affiliation>Department of Mathematics and Computer Science,  University of Oum El Bouaghi,  Laboratory of Dynamics systems and control,  ALGERIA</affiliation></person_name></contributors><jats:abstract xmlns:jats="http://www.ncbi.nlm.nih.gov/JATS1"><jats:p>Sentinel method introduced in the study of problems with incomplete data, particularly in the context of distributed systems where pollution terms may arise at the boundary. The idea of sentinel likely involves constructing a surrogate or placeholder value that helps account for missing data or uncertainties in the system. Weakly sentinel appears to be a modification or extension of the concept of a sentinel specifically tailored for estimating pollution terms in distributed systems with missing data. The term weakly might suggest that this sentinel is not as robust or precise as the ideal sentinel, but it serves a similar purpose in providing estimates or approximations in situations where complete data is not available.</jats:p></jats:abstract><publication_date media_type="online"><month>12</month><day>31</day><year>2023</year></publication_date><publication_date media_type="print"><month>12</month><day>31</day><year>2023</year></publication_date><pages><first_page>669</first_page><last_page>676</last_page></pages><publisher_item><item_number item_number_type="article_number">68</item_number></publisher_item><ai:program xmlns:ai="http://www.crossref.org/AccessIndicators.xsd" name="AccessIndicators"><ai:free_to_read start_date="2023-12-31"/><ai:license_ref applies_to="am" start_date="2023-12-31">https://wseas.com/journals/sac/2023/b385103-046(2023).pdf</ai:license_ref></ai:program><archive_locations><archive name="Portico"/></archive_locations><doi_data><doi>10.37394/23203.2023.18.68</doi><resource>https://wseas.com/journals/sac/2023/b385103-046(2023).pdf</resource></doi_data><citation_list><citation key="ref0"><doi>10.1111/j.1651-2227.2005.tb01779.x</doi><unstructured_citation>M. Rutter. Incidence of autism spectrum disorders: Changes over time and their meaning. Acta Paediatrica. 2007. https://doi.org/10.1111/j.1651- 2227.2005.tb01779.x </unstructured_citation></citation><citation key="ref1"><unstructured_citation>D.C. Bernard and E.G. Morton. Thermodynamics with Internal State Variables. J. Chem. Phys. 47, 597–613 (1967). https://doi.org/10.1063/1.1711937 </unstructured_citation></citation><citation key="ref2"><doi>10.1038/sj.onc.1208615</doi><unstructured_citation>S. Harris and A. Levine. The p53 pathway: positive and negative feedback loops. Oncogene 24, 2899–2908 (2005). https://doi.org/10.1038/sj.onc.1208615 </unstructured_citation></citation><citation key="ref3"><doi>10.1093/clinchem/39.5.766</doi><unstructured_citation>K. Emancipator and M.H. Kroll. A quantitative measure of nonlinearity. Clinical Chemistry, Volume 39, Issue 5, 1 May 1993, Pages 766– 772, https://doi.org/10.1093/clinchem/39.5.766 </unstructured_citation></citation><citation key="ref4"><doi>10.1007/bf03392013</doi><unstructured_citation>S. Dymond and R.A. Rehfeldt. Understanding complex behavior: The transformation of stimulus functions. BEHAV ANALYST 23, 239–254 (2000). https://doi.org/10.1007/BF03392013 </unstructured_citation></citation><citation key="ref5"><unstructured_citation>Y. Liu and H. Yu. A survey of underactuated mechanical systems. IET Control Theory and Applications. 2013. https://doi.org/10.1049/ietcta.2012.0505 </unstructured_citation></citation><citation key="ref6"><doi>10.1109/te.2022.3151376</doi><unstructured_citation>F. Cipparrone and D. Consonni. Calculation of Step Discontinuities in Electric Circuits: A Time-Domain Analysis. IEEE Transactions on Education. 65:4. (575- 583). Online publication date: 1-Nov-2022. https://doi.org/10.1109/TE.2022.3151376 </unstructured_citation></citation><citation key="ref7"><unstructured_citation>W.J. Stark. Nanoparticles in Biological Systems. Angewandte Chemie International Edition. 2011. https://doi.org/10.1002/anie.200906684 </unstructured_citation></citation><citation key="ref8"><doi>10.1016/j.jclepro.2015.09.007</doi><unstructured_citation>P. Ghisellini, C. Cialani and S. Ulgiati. A review on circular economy: the expected transition to a balanced interplay of environmental and economic systems. Journal of Cleaner Production. Volume 114, 15 February 2016, Pages 11-32. https://doi.org/10.1016/j.jclepro.2015.09.007 </unstructured_citation></citation><citation key="ref9"><doi>10.2307/2844197</doi><unstructured_citation>A. R. Radcliffe-Brown. On Social Structure. Royal Anthropological Institute of Great Britain and Ireland. Vol. 70, No. 1 (1940), pp. 1-12. https://doi.org/10.2307/2844197 </unstructured_citation></citation><citation key="ref10"><doi>10.1016/j.rser.2008.09.032</doi><unstructured_citation>S. He, Y. Li and R.Z. Wang. Progress of mathematical modeling on ejectors. Renewable and Sustainable Energy Reviews. Volume 13, Issue 8, October 2009, Pages 1760-1780. https://doi.org/10.1016/j.rser.2008.09.032 </unstructured_citation></citation><citation key="ref11"><doi>10.1139/t99-089</doi><unstructured_citation>H. Chen and C.F. Lee. Numerical simulation of debris flows. Canadian Geotechnical Journal. February 2000. https://doi.org/10.1139/t99-089 </unstructured_citation></citation><citation key="ref12"><doi>10.1146/annurev-fluid-122109-160718</doi><unstructured_citation>S. Pirozzoli. Numerical Methods for High-Speed Flows. Annual Review of Fluid Mechanics. Vol. 43:163-194. 2011. https://doi.org/10.1146/annurev-fluid-122109- 160718 </unstructured_citation></citation><citation key="ref13"><doi>10.1016/s0079-6123(06)65027-9</doi><unstructured_citation>S. Schaal and P. Mohajerian and A. Ijspeert. Dynamics systems vs. optimal control-a unifying view. Progress in Brain Research Volume 165, 2007, Pages 425-445. https://doi.org/10.1016/S0079-6123(06)65027- 9 </unstructured_citation></citation><citation key="ref14"><doi>10.1111/1744-7917.12405</doi><unstructured_citation>G. L. Lövei and M. Ferrante. A review of the sentinel prey method as a way of quantifying invertebrate predation under field conditions. Insect Science. 2016. https://doi.org/10.1111/1744-7917.12405 </unstructured_citation></citation><citation key="ref15"><doi>10.1115/1.3005099</doi><unstructured_citation>V. L. Rvachev and T. I. Sheiko. R-Functions in Boundary Value Problems in Mechanics. Appl. Mech. Rev. Apr 1995, 48(4): 151-188 (38 pages). https://doi.org/10.1115/1.3005099 </unstructured_citation></citation><citation key="ref16"><doi>10.1007/bf02179576</doi><unstructured_citation>R.E. Behrend, P.A. Pearce and D.L. O’Brien. Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy. J Stat Phys 84, 1–48 (1996). https://doi.org/10.1007/BF02179576 </unstructured_citation></citation><citation key="ref17"><doi>10.1177/1094428116641191</doi><unstructured_citation>C. Busse, A.P. Kach, and S.M. Wagner. Boundary Conditions: What They Are, How to Explore Them, Why We Need Them, and When to Consider Them. Volume 20, Issue 4, 2016. https://doi.org/10.1177/1094428116641191 </unstructured_citation></citation><citation key="ref18"><doi>10.1046/j.1525-1594.2002.07084.x</doi><unstructured_citation>O.F. Andreas, P.W. Walsh and J.E. Moore Jr. Computational Fluid Dynamics and Stent Design. Artificial Organs. 2002. https://doi.org/10.1046/j.1525- 1594.2002.07084.x </unstructured_citation></citation><citation key="ref19"><doi>10.1016/s0065-2156(08)70264-3</doi><unstructured_citation>R. Hill. Aspects of Invariance in Solid Mechanics. Advances in Applied Mechanics. Volume 18, 1979, Pages 1-75. https://doi.org/10.1016/S0065-2156(08)70264- 3 </unstructured_citation></citation><citation key="ref20"><doi>10.1146/annurev.fluid.30.1.365</doi><unstructured_citation>V. K. Dhir. Bolling Heat Transfer. Annual Review of Fluid Mechanics. Vol. 30:365-401, 1998. https://doi.org/10.1146/annurev.fluid.30.1.365 </unstructured_citation></citation><citation key="ref21"><unstructured_citation>E.J. Rothwell and M.J. Cloud. Electromagnetics. Journals. Taylor Francis. 2009. https://doi.org/10.1201/9781315222578 </unstructured_citation></citation><citation key="ref22"><doi>10.26907/0021-3446-2022-12-113-122</doi><unstructured_citation>B. Elhamza and A. Hafdallah. Identification of the potential coefficient in the wave equation with incomplete data: a sentinel method. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 12, Pages 113–122. DOI: https://doi.org/10.26907/0021- 3446-2022-12-113-122 </unstructured_citation></citation><citation key="ref23"><doi>10.37394/23203.2023.18.37</doi><unstructured_citation>N. Bouafi, N.L. Merabti and I. Rezzoug. Comparison Between the two HUM and No-regret Control Methods. WSEAS Transactions on Systems and Control, Volume 18, 2023. DOI: 10.37394/23203.2023.18.37 </unstructured_citation></citation><citation key="ref24"><doi>10.37394/23203.2022.17.53</doi><unstructured_citation>I. Rezzoug, A. Necib and T.E. Oussaeif. No Regret Control for Heat Equation With Delay and Incomplete Data. WSEAS Transactions on Systems and Control, Volume 17, 2022. DOI: 10.37394/23203.2022.17.53 </unstructured_citation></citation><citation key="ref25"><doi>10.1016/j.jde.2021.09.008</doi><unstructured_citation>M. Pinto and F. Poblete and D. Sepúlveda. Approximation of mild solutions of delay differential equations on Banach spaces. Journal of Differential Equations. Volume 303, 5 December 2021, Pages 156-182. https://doi.org/10.1016/j.jde.2021.09.008 </unstructured_citation></citation><citation key="ref26"><doi>10.37394/23202.2020.19.3</doi><unstructured_citation>I. Rezzoug and T.E. Oussaeif. Approximate Controllability. Wseas Transcations on Systems. Volume 19, (2020). DOI: 10.37394/23202.2020.19.3 </unstructured_citation></citation><citation key="ref27"><doi>10.1186/s13661-023-01708-3</doi><unstructured_citation>B. Elhamza and A. Hafdallah. Identification of the bulk modulus coefficient in the acoustic equation from boundary observation: a sentinel method. Bound Value Probl 2023, 23 (2023). https://doi.org/10.1186/s13661-023-01708-3 </unstructured_citation></citation><citation key="ref28"><doi>10.1016/j.jmps.2018.09.033</doi><unstructured_citation>Y. Lev and A. Faye and K.Y. Volokh. Thermoelastic deformation and failure of rubberlike materials.Journal of the Mechanics and Physics of Solids Volume 122, January 2019, Pages 538- 554. https://doi.org/10.1016/j.jmps.2018.09.033 </unstructured_citation></citation><citation key="ref29"><doi>10.1016/j.amc.2008.03.014</doi><unstructured_citation>Z. Wang and J. Liu. Identification of the pollution source from one-dimensional parabolic equation models. Applied Mathematics and Computation Volume 219, Issue 8, 15 December 2012, Pages 3403-3413. https://doi.org/10.1016/j.amc.2008.03.014 </unstructured_citation></citation><citation key="ref30"><doi>10.1016/b978-0-08-100037-3.00005-5</doi><unstructured_citation>J.P. Nunes and J.F. Silva. 5 - Sandwiched composites in aerospace engineering. Advanced Composite Materials for Aerospace Engineering. Processing, Properties and Applications. 2016, Pages 129-174. https://doi.org/10.1016/B978-0-08-100037- 3.00005-5 </unstructured_citation></citation><citation key="ref31"><unstructured_citation>G.M. Whitesides. Soft Robotics. Angewandte Chemie. 2018. https://doi.org/10.1002/anie.201800907 </unstructured_citation></citation><citation key="ref32"><doi>10.1257/jel.20171452</doi><unstructured_citation>G. Avi and C. Tucker. 2019. ”Digital Economics.” Journal of Economic Literature, 57 (1): 3-43. DOI: 10.1257/jel.20171452 </unstructured_citation></citation><citation key="ref33"><doi>10.1146/annurev-financial-092214-043752</doi><unstructured_citation>D. Hirshleifer. Behavioral Finance. Annual Review of Financial Economics. Vol. 7:133- 159, 2015. https://doi.org/10.1146/annurevfinancial-092214-043752 </unstructured_citation></citation><citation key="ref34"><doi>10.1023/a:1008930403506</doi><unstructured_citation>M.G. Mehrabi, A.G. Ulsoy and Y. Koren. Reconfigurable manufacturing systems: Key to future manufacturing. Journal of Intelligent Manufacturing 11, 403–419 (2000). https://doi.org/10.1023/A:1008930403506 </unstructured_citation></citation><citation key="ref35"><doi>10.37394/232011.2022.17.29</doi><unstructured_citation>A. Benbrahim and I. Rezzoug and A. Necib. A revision of M. Asch notion of Discrete control. Wseas Transcations on Applied and Theorical Mechanics. Volume 17, (2022). DOI: 10.37394/232011.2022.17.29 </unstructured_citation></citation><citation key="ref36"><doi>10.1016/bs.hna.2021.12.004</doi><unstructured_citation>E. Casas and K. Kunisch and F. Tröltzsch. Chapter 4 - Optimal control of PDEs and FE-approximation. Handbook of Numerical Analysis Volume 23, 2022, Pages 115-163. https://doi.org/10.1016/bs.hna.2021.12.004 </unstructured_citation></citation><citation key="ref37"><doi>10.1016/j.camwa.2014.07.007</doi><unstructured_citation>A. Akkouche and A. Maidi and M. Aidene. Optimal control of partial differential equations based on the Variational Iteration Method. Computers Mathematics with Applications Volume 68, Issue 5, September 2014, Pages 622-631. https://doi.org/10.1016/j.camwa.2014.07.007 </unstructured_citation></citation><citation key="ref38"><doi>10.1016/s0377-0427(00)00418-0</doi><unstructured_citation>R.W.H. Sargent. Optimal control. Journal of Computational and Applied Mathematics. Volume 124, Issues 1–2, 1 December 2000, Pages 361-371. https://doi.org/10.1016/S0377- 0427(00)00418-0 </unstructured_citation></citation><citation key="ref39"><unstructured_citation>H. L. Trentelman. Controllability and Observability. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. 2014. https://doi.org/10.1007/978-1-4471- 5102-9-192-1 </unstructured_citation></citation><citation key="ref40"><unstructured_citation>J.L. Lions. Controllability, Penalty and stiffness, Anal, Nor, Serie 4, Tome 25, N3-4. PP. 547-610, 1997. </unstructured_citation></citation><citation key="ref41"><doi>10.1007/978-3-319-49631-3_1</doi><unstructured_citation>E. Casas and M. Mateos. Optimal Control of Partial Differential Equations. In: Mateos, M., Alonso, P. (eds) Computational Mathematics, Numerical Analysis and Applications. SEMA SIMAI Springer Series, vol 13. Springer, Cham. 2017. https://doi.org/10.1007/978-3- 319-49631-3-1 </unstructured_citation></citation><citation key="ref42"><doi>10.1142/s021820259700044x</doi><unstructured_citation>O. Bodart and P. Demeestere. Sentinels for the identification of an unknown boundary. University of Compiegne (France). M3AS, 7(6), pp. 871-885. 1997. </unstructured_citation></citation><citation key="ref43"><unstructured_citation>L. Afifi, A.El Jai and E. Zerrik. Systems Theory : Modelling, Analysis and Control. FES2009 Proceedings. PUP, ISBN : 978-2-35412-043-6, 2009.</unstructured_citation></citation></citation_list></journal_article></journal></body></doi_batch>