Analysis and geometry in control theory and its applications

Since the 1950s Control Theory has established itself as a powerful mathematical discipline, particularly suitable for applications in a number of applied research fields, including advanced engineering design, economics and medical sciences. However, since the emerging of this discipline, the need of rethinking and extending fields such as Calculus of Variations, Differential Geometry, Nonsmooth Analysis is permanently parallel to investigations devoted to applications. Nowadays Control Theory qualifies as a rich source of basic abstract problems arising from applications as well as an important perspective to investigate purely mathematical issues. In many fields of mathematics, a huge and growing volume of activity has been accompanied by fragmentation into a multitude of narrow specialities. But outstanding advances are many times the end-result of the quest for unifying themes and a synthesis of different approaches. Control Theory and its Applications is no exception. Here, the fruitful interplay of analysis and geometry has had a crucial role in the evolution of the field. This volume collects some recent results, highlighting geometrical and analytical aspects and the connections between them. Applications are in the background and sometimes explicitly treated, in the classical spirit of a mutual interplay occurring between abstract theory and problem-solving practice.