Abstract
This paper extends some existence theorems of Cesari for optimal control problems to systems whose dynamics is described by functional differential equations of finitely-retarded type. We show that the proper choice of state space is the spaceE1×C[−τ, 0], where τ>0 represents the time-lag of the system, and that it is necessary to choose initial conditions from a compact set inC[−τ, 0] as well as to employ the usual growth condition.
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