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Sufficient conditions for optimal control problems with mixed constraints
Author(s) -
Galewska E.,
Nowakowski A.
Publication year - 2005
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.762
Subject(s) - optimal control , dynamic programming , dual (grammatical number) , mathematical optimization , class (philosophy) , neighbourhood (mathematics) , trajectory , set (abstract data type) , state (computer science) , bellman equation , mathematics , function (biology) , control (management) , computer science , control theory (sociology) , algorithm , art , mathematical analysis , physics , literature , astronomy , artificial intelligence , evolutionary biology , biology , programming language
In this paper we derive sufficient conditions for optimal control problems with mixed control and state constraints by applying a dual approach to the dynamic programming. These conditions guarantee that a relative minimum is achieved. We seek an optimal pair in the class of those admissible pairs for which graphs of trajectories belong to a set defined by a function satisfying a dual equation of dynamic programming. This set usually differs from the classical neighbourhood of an optimal trajectory. We prove a verification theorem and introduce an optimal dual feedback control. Copyright © 2005 John Wiley & Sons, Ltd.