Nonlinear differential equations of Riccati type on ordered Banach spaces
| Autor: | Vasile Dragan, Viorica Mariela Ungureanu |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
maximal
riccati equations Mathematical analysis Banach space stabilizability Linear-quadratic regulator Optimal control Linear-quadratic-Gaussian control Multiplicative noise Algebraic Riccati equation QA1-939 Riccati equation Applied mathematics minimal and stabilizing solutions C0-semigroup Mathematics |
| Zdroj: | Electronic Journal of Qualitative Theory of Differential Equations, Vol 2012, Iss 17, Pp 1-22 (2012) |
| DOI: | 10.14232/ejqtde.2012.3.17 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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