The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form:
${\displaystyle\inf_{{\displaystyle(u,v)\in {\cal U}_{ad}}} \int_{0}^{1} f\left(t, u(\theta_v(t)),u^{\prime}(t),v(t)\right){\rm d}t}$
, (1)
where ${\cal U}_{ad} $
is a set of admissible controls and $\theta_v$
is the solution of the following equation:
$\{ \frac{{\rm d}\theta(t)}{{\rm d}t}=g(t,\theta(t),v(t)), t\in [0,1]$
;
$\displaystyle\theta(0)=\theta_0, \theta(t)\in [0,1] \forall t$
. (2).
The results are nonlocal and new.