Dynamic optimization problems with free-time and active state constraints

Free-time dynamic optimization problems are treated with state constraints in which the data is permitted to be measurable with respect to the time variable. Necessary conditions for such problems have previously been derived only under the assumption that the state constraint is inactive at the optimal endtimes. A more detailed analysis than has yet been undertaken of the interaction between the optimal free endtimes and the state constraint permits the removal of this assumption. An example clarifies the nature of the new necessary condition.