ABSTRACT
In Optimal Control Theory not only is this one of the basic issues to address, but it also stands prominent as the possible key to close the large gaps which still exist between existence theory on one side and between necessary and sufficient conditions for optimality on the other. The techniques of existence theory usually require to work on large function spaces and therefore only give existence of a solution in these spaces, measurable functions being the most regular one can do. The standard necessary conditions for optimality, such as the Pontryagin Maximum Principle, put certain restrictions on the structure of optimal controls. In particular instances these conditions may also yield information about regularity properties, but they fail to do so in general. The 'geometric technique', based on the concept of conjugate points, is a generalization of the classical envelope techniques of calculus of variations to optimal control theory due to H. J. Sussmann.
