  We consider cost minimising control problems, in which the dynamical system
is constrained by higher order differential equations of Euler-Lagrange type.
Following ideas from a previous paper by the first and the third author, we
prove that a curve of controls $u_o(t)$ and a set of initial conditions
$\sigma_o$ gives an optimal solution for a control problem of the considered
type if and only if an appropriate double integral is greater than or equal to
zero along any homotopy $(u(t, s), \sigma(s))$ of control curves and initial
data starting from $u_o(t) = u(t, 0)$ and $\sigma_o = \sigma(0)$. This property
is called "Principle of Minimal Labour". From this principle we derive a
generalisation of the classical Pontryagin Maximum Principle that holds under
higher order differential constraints of Euler-Lagrange type and without the
hypothesis of fixed initial data.
