Contingent solutions for the Bellmann equation in infinite dimensions (Q1584021)
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scientific article; zbMATH DE number 1523629
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Contingent solutions for the Bellmann equation in infinite dimensions |
scientific article; zbMATH DE number 1523629 |
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Contingent solutions for the Bellmann equation in infinite dimensions (English)
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5 February 2001
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The author considers the minimum time problem for an infinite dimensional linear control system on a reflexive Banach space. Under certain conditions (among which is the continuity of the optimal control function at \(t=0\)) the author proves that the minimum time function as well as its Kruzkov transformation are contingent solutions of the respective Hamilton-Jacobi-Bellman equations. An important ingredient of the proof are viability properties of the hypograph of the minimum time functions under the semigroup generated by the considered system.
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minimum time problem
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infinite dimensional system
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Hamilton-Jacobi-Bellman equation
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contingent solution
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viability
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optimal control
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hypograph
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