Control problems with differential constraints of higher order

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, we prove that curve controls uo(t) and set initial conditions σo give an optimal solution for problem considered type if only appropriate double integral greater than or equal to zero along any homotopy (u(t,s),σ(s)) curves data starting uo(t)=u(t,0) σo=σ(0). This property called Principle Minimal Labour. From this principle derive generalisation classical Pontryagin Maximum holds under constraints without hypothesis fixed data.