{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T14:11:31Z","timestamp":1656079891472},"reference-count":50,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2022,4,26]],"date-time":"2022-04-26T00:00:00Z","timestamp":1650931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,6,24]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We study a class of infinite horizon optimal control problems with a state delay, and investigate the dynamic programming approach which leverages the sufficient optimality conditions and provides a closed-loop solution. Importantly, the well-known Lyapunov\u2013Krasovskii functional is applied to relate the solution of the problem to the solution of a set of three Riccati-type matrix differential equations. We then present an analytic-based approach to solve the resultant equations and subsequently provide a suboptimal closed-loop solution for the considered problem. We prove the uniform convergence of the proposed approach and show that the presented closed-loop system is asymptotically stable in the Lyapunov sense. Furthermore, the observability of the linear time-delay system is discussed and proved. Finally, numerical examples illustrate the efficiency of the proposed method.<\/jats:p>","DOI":"10.1093\/imamci\/dnac002","type":"journal-article","created":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T13:21:09Z","timestamp":1651065669000},"page":"675-707","source":"Crossref","is-referenced-by-count":0,"title":["A suboptimal control of linear time-delay problems via dynamic programming"],"prefix":"10.1093","volume":"39","author":[{"given":"Atefeh","family":"Gooran Orimi","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Ferdowsi University of Mashhad , Mashhad 9177548953 , Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sohrab","family":"Effati","sequence":"additional","affiliation":[{"name":"Center of Excellence on Soft Computing and Intelligent Information Processing (SCIIP), Ferdowsi University of Mashhad , Mashhad 9177948974 , Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Hadi","family":"Farahi","sequence":"additional","affiliation":[{"name":"The Center of Excellence on Modeling and Control Systems (CEMCS) , Mashhad 917751111 , Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,4,26]]},"reference":[{"key":"2022062413512553100_ref1","doi-asserted-by":"crossref","first-page":"2717","DOI":"10.23919\/ACC45564.2020.9147576","volume-title":"2020 American Control Conference (ACC)","author":"Amini","year":"2020"},{"key":"2022062413512553100_ref2","volume-title":"Optimal control: linear quadratic methods","author":"Anderson","year":"2007"},{"key":"2022062413512553100_ref3","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.eswa.2019.05.035","article-title":"Social mimic optimization algorithm and engineering applications","volume":"134","author":"Balochian","year":"2019","journal-title":"Expert Systems with Applications"},{"key":"2022062413512553100_ref4","volume-title":"Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations","author":"Bardi","year":"2008"},{"key":"2022062413512553100_ref5","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1126\/science.153.3731.34","article-title":"Dynamic programming","volume":"153","author":"Bellman","year":"1966","journal-title":"Science"},{"key":"2022062413512553100_ref6","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1007\/s11424-020-8185-1","article-title":"Stochastic optimal control problem in advertising model with delay","volume":"33","author":"Chen","year":"2020","journal-title":"Journal of Systems Science and Complexity"},{"key":"2022062413512553100_ref7","volume-title":"Optimal control of stochastic functional differential equations with application to finance","author":"Coayla-Teran","year":"2014"},{"key":"2022062413512553100_ref8","first-page":"451","article-title":"Numerical solution of time delay optimal control problems by hybrid of block-pulse functions and Bernstein polynomials","volume":"35","author":"Dadkhah","year":"2018","journal-title":"IMA J. 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