DYNAMIC-PROGRAMMING FOR FREE-TIME PROBLEMS WITH END-POINT CONSTRAINTS

If we are able to find a local verification function associated with a n admissible trajectory x(.), then x(.) is a local minimizer. It is of interest therefore to know when such local verification functions exi st. In this paper it is shown that the existence of a local verificati on function is necessary for x(.) to be a local minimizer, under a nor mality hypothesis. The novelty of these results is that they treat pro blems with a general endpoint constraint and where the endtime is a ch oice variable. Here the value function of the original problem does no t serve as a local verification function; instead it must be construct ed from some derived problem. The data are allowed to be measurable in the time variable, and the normality hypothesis is expressed in terms of recent free-endtime necessary conditions of optimality for problem s with measurable time dependence.