The Importance of the Realization of Nonlinear ODEs in Optimal Control Problems

This paper shows that, when an optimal control problem is characterized by a differential equation in which the time derivatives of the input are involved, a procedure for lowering the order of these derivatives makes the optimal control problem more tractable both from the theoretical point of view, reducing the number of states (and co-states, if Pontryagin principle is followed), and from the numerical point of view, leading to faster methods. The procedure is explicitly applied to an academic example as well as to an optimization problem borrowed from the structural mechanics.