The Maximum Principle for an Optimal Solution to a Differential Inclusion with End Points Constraints
Author:
- 1 January 1987
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 25 (1) , 145-157
Abstract
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.Keywords
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