A Course on Geometric Control Theory: Transitivity and minimal sets

The basic conception of control system emerged in the 2nd century with the interest of regulating devices. The control theory became an interdisciplinary branch of engineering and mathematics and its development has influenced the advancement of technology and science. The accessible mathematical formulation of control system has enabled extensive applications to natural and social sciences. This book is a short course on control theory in the geometric point of view, designed for students and professionals interested in the fundamental theory of control systems. The proposal is to introduce the geometric control theory by exploring the notions of transitivity and controllability together with the notions of minimal sets and the elements of the Conley dynamical theory. The reader will find the book an accessible source of basic definitions, properties, examples, classical theorems, references, and list of exercises.