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The Maximum Principle for an Optimal Solution to a Differential Inclusion with End Points Constraints

Frankowska, Halina (1987), The Maximum Principle for an Optimal Solution to a Differential Inclusion with End Points Constraints, SIAM Journal on Control and Optimization, 25, 1, p. 145-157. http://dx.doi.org/10.1137/0325010

Type
Article accepté pour publication ou publié
Date
1987
Journal name
SIAM Journal on Control and Optimization
Volume
25
Number
1
Publisher
SIAM
Pages
145-157
Publication identifier
Metadata
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Author(s)
Frankowska, Halina
Abstract (EN)
We derive Pontryagin’s maximum principle for a general optimal control problem using the set-valued version of variational equation. We achieve this aim by exploiting an adequate differential calculus of set-valued maps. Furthermore, the calmness condition is replaced by a surjectivity condition involving reachable sets of the “set-valued linearization” of the initial control problem. Duality then provides both the “adjoint differential inclusion” and the maximum principle.
Subjects / Keywords
differential inclusion; tangent cone; derivative of a set-valued map; convex process; variational inclusion; maximum principle