Optimal Control

  • Richard Vinter

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Richard Vinter
    Pages 1-60
  3. Richard Vinter
    Pages 109-126
  4. Richard Vinter
    Pages 127-177
  5. Richard Vinter
    Pages 179-199
  6. Richard Vinter
    Pages 201-231
  7. Richard Vinter
    Pages 397-434
  8. Richard Vinter
    Pages 435-491
  9. Back Matter
    Pages 493-507

About this book


Optimal Control brings together many of the important advances in 'nonsmooth' optimal control over the last several decades concerning necessary conditions, minimizer regularity, and global optimality conditions associated with the Hamilton–Jacobi equation. The book is largely self-contained and incorporates numerous simplifications and unifying features for the subject’s key concepts and foundations.

Features and Topics:

* a comprehensive overview is provided for specialists and nonspecialists

* authoritative, coherent, and accessible coverage of the role of nonsmooth analysis in investigating minimizing curves for optimal control

* chapter coverage of dynamic programming and the regularity of minimizers

* explains the necessary conditions for nonconvex problems

This book is an excellent presentation of the foundations and applications of nonsmooth optimal control for postgraduates, researchers, and professionals in systems, control, optimization, and applied mathematics.


Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control.—Mathematical Reviews

This remarkable book presents Optimal Control seen as a natural development of Calculus of Variations so as to deal with the control of engineering devices. ... Thanks to a great effort to be self-contained, it renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis). —Automatica

The book may be an essential resource for potential readers, experts in control and optimization, as well as postgraduates and applied mathematicians, and it will be valued for its accessibility and clear exposition.—Applications of Mathematics


Differential inclusions Dynamic programming Euler–Lagrange condition Hamilton condition Hamilton-Jacobi equation Maximum principle Minimizers Nonlinear control Nonsmooth analysis Nonsmoothness calculus optimal control optimization programming

Authors and affiliations

  • Richard Vinter
    • 1
  1. 1.Dept. Electrical & Electronic, EngineeringImperial College LondonLondonUnited Kingdom

Bibliographic information