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Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, economics and the medical sciences. However, since its emergence, there has been a need to rethink and extend fields such as calculus of variations, differential geometry and nonsmooth analysis, which are closely tied to research on applications. Today control theory is a rich source of basic abstract problems arising from applications, and provides an important frame of reference for investigating purely mathematical issues. In many fields of mathematics, the huge and growing scope of activity has been accompanied by fragmentation into a multitude of narrow specialties. However, outstanding advances are often the result of the quest for unifying themes and a synthesis of different approaches. Control theory and its applications are no exception. Here, the interaction between analysis and geometry has played a crucial role in the evolution of the field. This book collects some recent results, highlighting geometrical and analytical aspects and the possible connections between them. Applications provide the background, in the classical spirit of mutual interplay between abstract theory and problem-solving practice.

Operations Research --- Calculus --- Civil & Environmental Engineering --- Mathematics --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Control theory --- Geometry. --- Mathematical models. --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Calculus of variations. --- Control engineering. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Analysis. --- Applications of Mathematics. --- Control. --- Euclid's Elements --- Mathematical optimization. --- Systems theory. --- Global analysis (Mathematics). --- Control and Systems Theory. --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers --- Engineering --- Engineering analysis --- 517.1 Mathematical analysis --- Systems, Theory of --- Systems science --- Isoperimetrical problems --- Variations, Calculus of --- Philosophy