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. Inhaltsverzeichnis Some Preliminaries in Functional Analysis.- Controllability of Linear Systems.- The Minimum Time and the Minimum Norm for Linear Control Systems.- Maximum Principles.- Semilinear Control Systems.- The Minimum-Time Function for Mulitvalued Semilinear Evolutions. Autorenportrait Ovidiu Cârja is a professor at the Alexandru Ioan Cuza University of Ia i and a researcher at the Romanian Academy, Ia i Branch. His research interests include controllability and time-optimal control for linear and nonlinear systems in Banach spaces, feedback controls, Lyapunov pairs, and viability and invariance theory. He is a coauthor of a monograph on viability, invariance, and applications published by Elsevier in 2007. Alina Ilinca Lazu is an associate professor at the Gheorghe Asachi Technical University of Ia i. Her research focuses on time-optimal controllability, with particular attention paid to feedback controls and Lyapunov pairs. She has also contributed to the study of near viability for nonlinear differential inclusions.