Time-Optimal Control and Controllability in Banach Spaces

This monograph develops a unified approach to some central questions of control theory in infinite-dimensional settings: whether a system can be steered to a desired state, how rapidly this can be achieved, and how much control effort is required. Working within the general framework of Banach spaces, it brings together controllability theory, minimum-time control, and minimum-norm control, emphasizing the relationships between these problems and the value functions that characterize them. Particular attention is given to quantitative estimates, maximum principles, and dynamic programming methods, which are developed in a common analytical framework and used to derive regularity and optimality results. The treatment also extends from linear systems to semilinear evolutions and differential inclusions, demonstrating that the underlying ideas remain effective in the presence of nonlinearities, uncertainties, and multivalued dynamics. Combining classical results with original research by the authors, this monograph provides both a coherent reference for researchers and an advanced introduction for graduate students working in infinite-dimensional control theory and optimization.