| Abstract: | The higher-order tests for optimality of singular arcs in optimal control problems, as well as the characterization of the continuity and smoothness properties of the optimal control at points, called junctions, joining nonsingular and singular arcs of the control, depend upon the orders of the arcs involved. To data, definitions of order have been rigorously given only for terminal unconstrained control problems or by means of a normality assumption in the order cases. We give here a new definition of the local order of a singular arc which unifies those already given in the literature. One advantage of the proposed definition is that, unlike the previous ones, it remains valid even when there are terminal constraints. One example will illustrate the fact that such a basic concept is essential to solve the very difficult synthesis problem as soon as the dimension of the state space is greater than two. |
