The mean‐field linear quadratic optimal control problem for stochastic systems controlled by impulses
In the present note, we state and solve the linear quadratic (LQ) control problem for a class of McKean–Vlasov stochastic differential equations for which the control actions are of impulsive nature. After reformulating the original optimization problem using an orthogonal decomposition of the state...
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| Published in | Asian journal of control Vol. 26; no. 2; pp. 575 - 583 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
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01.03.2024
Asian Control Association (ACA) and Chinese Automatic Control Society (CACS) |
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| ISSN | 1561-8625 1934-6093 |
| DOI | 10.1002/asjc.3214 |
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| Abstract | In the present note, we state and solve the linear quadratic (LQ) control problem for a class of McKean–Vlasov stochastic differential equations for which the control actions are of impulsive nature. After reformulating the original optimization problem using an orthogonal decomposition of the state variables, we introduce an adequately defined system of two coupled matrix Lyapunov‐type differential equations with jumps. Such equations are central for the definition of the optimal feedback gains corresponding to the closed‐loop representation of the optimal LQ control. |
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| AbstractList | In the present note, we state and solve the linear quadratic (LQ) control problem for a class of McKean–Vlasov stochastic differential equations for which the control actions are of impulsive nature. After reformulating the original optimization problem using an orthogonal decomposition of the state variables, we introduce an adequately defined system of two coupled matrix Lyapunov‐type differential equations with jumps. Such equations are central for the definition of the optimal feedback gains corresponding to the closed‐loop representation of the optimal LQ control. |
| Author | Dragan, Vasile Aberkane, Samir |
| Author_xml | – sequence: 1 givenname: Vasile surname: Dragan fullname: Dragan, Vasile organization: Institute of Mathematics “Simion Stoilow” of the Romanian Academy Bucharest Romania, The Academy of the Romanian Scientists Bucharest Romania – sequence: 2 givenname: Samir orcidid: 0000-0002-8657-6689 surname: Aberkane fullname: Aberkane, Samir organization: Université de Lorraine, CRAN, UMR 7039 Vandœvre‐lés‐Nancy France, CNRS, CRAN, UMR 7039 Vandœvre‐lés‐Nancy France |
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| Cites_doi | 10.1007/s00245-010-9123-8 10.1287/moor.15.4.676 10.1109/TAC.2022.3202824 10.1137/050645944 10.1090/tran/6502 10.1137/S0363012900371083 10.1214/aop/1176988866 10.1080/01630560802580679 10.1007/978-1-4614-8663-3 10.1016/j.spa.2009.05.002 10.1007/s00245-011-9136-y 10.1080/07362994.2010.482836 10.1016/j.sysconle.2020.104624 10.1137/0117041 10.1016/j.jde.2021.06.004 10.1051/cocv/2016023 10.1017/S0305004100030929 10.1214/08-AOP442 10.1007/BF00939533 10.1016/j.automatica.2020.109067 10.1109/TCST.2016.2604739 10.4310/CIS.2006.v6.n3.a5 10.1080/17442508.2011.651619 10.3934/mcrf.2015.5.97 10.1007/BF00940627 10.1017/S1446788700029384 10.1137/S0363012900367825 10.1016/0304-4149(92)90138-G 10.1016/0304-4149(95)00050-X 10.1007/s001860050083 10.1137/120892477 10.1016/j.automatica.2012.06.082 |
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| SubjectTerms | Automatic Differential equations Engineering Sciences Mathematical analysis Optimal control Stochastic systems |
| Title | The mean‐field linear quadratic optimal control problem for stochastic systems controlled by impulses |
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