Nonlinear differential equations of Riccati type on ordered Banach spaces
In this paper we consider a general class of time-varying nonlinear differential equations on infinite dimensional ordered Banach spaces, which includes as special cases many known differential Riccati equations of optimal control. Using a linear matrix inequalities (LMIs) approach we provide necess...
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| Format: | Article |
| Language: | English |
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University of Szeged
2012-05-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1059 |
| _version_ | 1827951320043094016 |
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| author | V. M. Ungureanu V. Dragan |
| author_facet | V. M. Ungureanu V. Dragan |
| author_sort | V. M. Ungureanu |
| collection | DOAJ |
| description | In this paper we consider a general class of time-varying nonlinear differential equations on infinite dimensional ordered Banach spaces, which includes as special cases many known differential Riccati equations of optimal control. Using a linear matrix inequalities (LMIs) approach we provide necessary and sufficient conditions for the existence of some global solutions such as maximal, stabilizing and minimal solutions for this class of generalized Riccati equations. The obtained results extend to infinite dimensions and unify corresponding results in the literature. They provide useful tools for solving infinite-time linear quadratic (LQ) control problems for linear differential systems affected by countably-infinite-state Markovian jumps and/or multiplicative noise. |
| first_indexed | 2024-04-09T13:39:55Z |
| format | Article |
| id | doaj.art-dc0b5f8973a6471691aee63216312d0d |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:55Z |
| publishDate | 2012-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-dc0b5f8973a6471691aee63216312d0d2023-05-09T07:53:03ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752012-05-0120121712210.14232/ejqtde.2012.3.171059Nonlinear differential equations of Riccati type on ordered Banach spacesV. M. Ungureanu0V. Dragan1Constantin Brancusi University, Targu-Jiu, RomaniaInstitute of Mathematics of the Romanian Academy, Bucharest, RomaniaIn this paper we consider a general class of time-varying nonlinear differential equations on infinite dimensional ordered Banach spaces, which includes as special cases many known differential Riccati equations of optimal control. Using a linear matrix inequalities (LMIs) approach we provide necessary and sufficient conditions for the existence of some global solutions such as maximal, stabilizing and minimal solutions for this class of generalized Riccati equations. The obtained results extend to infinite dimensions and unify corresponding results in the literature. They provide useful tools for solving infinite-time linear quadratic (LQ) control problems for linear differential systems affected by countably-infinite-state Markovian jumps and/or multiplicative noise.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1059riccati equationsstabilizabilitymaximalminimal and stabilizing solutions |
| spellingShingle | V. M. Ungureanu V. Dragan Nonlinear differential equations of Riccati type on ordered Banach spaces Electronic Journal of Qualitative Theory of Differential Equations riccati equations stabilizability maximal minimal and stabilizing solutions |
| title | Nonlinear differential equations of Riccati type on ordered Banach spaces |
| title_full | Nonlinear differential equations of Riccati type on ordered Banach spaces |
| title_fullStr | Nonlinear differential equations of Riccati type on ordered Banach spaces |
| title_full_unstemmed | Nonlinear differential equations of Riccati type on ordered Banach spaces |
| title_short | Nonlinear differential equations of Riccati type on ordered Banach spaces |
| title_sort | nonlinear differential equations of riccati type on ordered banach spaces |
| topic | riccati equations stabilizability maximal minimal and stabilizing solutions |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1059 |
| work_keys_str_mv | AT vmungureanu nonlineardifferentialequationsofriccatitypeonorderedbanachspaces AT vdragan nonlineardifferentialequationsofriccatitypeonorderedbanachspaces |