Calculus of Variations and Control Theory Chapman & Hall/CRC Monographs and Research Notes in Mathematics Series

This work is an introduction in the classical theory of calculus of variations and the theory of control of differential equations. The purpose of the book is to present classic theory, to describe the geometric and analytic setting of the problems, to study the specific mathematical methods and the underlying Hamiltonian formalism corresponding to both branches, as well to discuss all these facts in concrete situations. It is addressed especially to the students in mathematics and physics but may be useful to anybody wishing a relatively rapid introduction in the various branches and directions of study of the field.

Introduction. Fundamentals of differential geometry. The fundamental problem in calculus of variations. Hamiltonian formalism. Geometric calculus of variations. Control of linear systems. Geometric approach to optimal control problems. Controllability of differential systems. Semigroups of operators and evolution equations. Convex optimization and convex control problems. Linearquadratic optimal control problems for parabolic type equations. Controllability of parabolic equations and systems. Stabilization of parabolic type systems.

Catalin Lefter is a Professor in the department of Mathematics at Al. I . Cuza University, Romania. His main areas of interest lies in Partial Differential Equations and Control Theory.