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How to state necessary optimality conditions for control problems with deviating arguments?

Lassana Samassi, Rabah Tahraoui (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: inf ( u , v ) 𝒰 a d 0 1 f t , u ( θ v ( t ) ) , u ' ( t ) , v ( t ) d t , (1) where 𝒰 a d is a set of admissible controls and θ v is the solution of the following equation: { d θ ( t ) d t = g ( t , θ ( t ) , v ( t ) ) , t [ 0 , 1 ] ; θ ( 0 ) = θ 0 , θ ( t ) [ 0 , 1 ] t . (2). The results are nonlocal and new.

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