The second volume introduces the reader to the theory of optimal control and to the theory of variation, reflected in many mathematical, physical, technical and economical problems. It is designed to improve the education of engineers more than mathematicians, so not all theorems are proven; there is more attention on the approach, the problems and the ideas than on the technique. Being devoted to the problem of minimization of functionals, this volume systematically treats diverse formulations of optimal control, existence of solutions, the necessary conditions, the sufficient conditions and the Pontrjagin minimum principle. Many interesting and useful examples of solutions to diverse minimization problems are discussed. The book is based on lectures taught by the author in a Masters program of variation analysis and control. Like the first volume, this one is skilfully compiled and treated. The whole book is a valuable contribution to the literature in this branch of mathematics.

Reviewer:

jdr