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Optimality Conditions and Synthesis for the Minimum Time Problem

Cannarsa, Piermarco; Frankowska, Halina; Sinestrari, Carlo (2000), Optimality Conditions and Synthesis for the Minimum Time Problem, Set-Valued Analysis, 8, 1-2, p. 127-148. http://dx.doi.org/10.1023/A:1008726610555

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Type
Article accepté pour publication ou publié
Date
2000
Journal name
Set-Valued Analysis
Volume
8
Number
1-2
Publisher
Springer
Pages
127-148
Publication identifier
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Author(s)
Cannarsa, Piermarco
Frankowska, Halina
Sinestrari, Carlo
Abstract (EN)
We study the minimum time optimal control problem for a nonlinear system in R n with a general target. Necessary and sufficient optimality conditions are obtained. In particular, we describe a class of costates that are included in the superdifferential of the minimum time function, even in the case when this function is only lower semicontinuous. Two set-valued maps are constructed to provide time optimal synthesis.
Subjects / Keywords
minimum time function; optimal synthesis; differential inclusions; Hamilton–Jacobi equations; viability theory; viscosity solutions