Control and Observation Problems in Banach Spaces. Optimal Control and Maximum Principle. Applications to Ordinary Differential Equations in ℝn
Autor: | A. I. Prilepko |
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Rok vydání: | 2019 |
Předmět: |
Mathematics::Functional Analysis
0209 industrial biotechnology Partial differential equation General Mathematics 010102 general mathematics Banach space 02 engineering and technology Optimal control 01 natural sciences Controllability 020901 industrial engineering & automation Maximum principle Adjoint equation Applied mathematics Observability Uniqueness 0101 mathematics Analysis Mathematics |
Zdroj: | Differential Equations. 55:1630-1640 |
ISSN: | 1608-3083 0012-2661 |
DOI: | 10.1134/s0012266119120097 |
Popis: | In a Banach space, we study an equation of the first kind as an observation problem, with the adjoint equation considered as a control problem. The Banach uniqueness and existence method and the monotone mapping method are applied to the study of these observation and control problems. For the case of reflexive Banach spaces, a controllability criterion and an abstract maximum principle are proved. In particular, it is established that continuous observability implies the existence and uniqueness of the solution of the inverse controllability problem and an estimate for the solution. |
Databáze: | OpenAIRE |
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