In this paper, a new method for model based optimal tracking control is presented.
The special composition of the cost functional leads to design parameters for constraining the
solution so as to ensure that machine limitations are not violated. By minimizing the cost
functional with the calculus of variations, or more precisely the Euler-Lagrange equations, the
state space representation of the system dynamics is transformed into an augmented state
space representation describing the optimal tracking dynamics. The optimal control input is
numerically calculated by solving the set of dierential equations, given by the augmented state
space system, globally with a specialized least-squares solver. The general control approach is
demonstrated on an underactuated crane-like system with xed load hoisting length operating
in the horizontal plane. In this case the introduced design parameters determine the tradeo
between the cost of tracking accuracy and the cost of using large values of crane speed
and acceleration. The potential of the proposed control scheme is proven by both simulation
and experimental tests. The multibody simulation is carried out with the software Simscape
MultibodyTM. For the experimental verication an industrial robot is used whose end eector
only moves in a horizontal plane to imitate the trolley of an overhead crane.