Optimal Control with Engineering Applications - Softcover

Geering, Hans P.

Softcover

ISBN 10: 3540694374 ISBN 13: 9783540694373

Publisher: Springer, 2007

Synopsis

This book introduces a variety of problem statements in classical optimal control, in optimal estimation and filtering, and in optimal control problems with non-scalar-valued performance criteria. Many example problems are solved completely in the body of the text. All chapter-end exercises are sketched in the appendix. The theoretical part of the book is based on the calculus of variations, so the exposition is very transparent and requires little mathematical rigor.

About this title

From the Back Cover

Because the theoretical part of the book is based on the calculus of variations, the exposition is very transparent and requires mostly a trivial mathematical background. In the case of open-loop optimal control, this leads to Pontryagin’s Minimum Principle and, in the case of closed-loop optimal control, to the Hamilton-Jacobi-Bellman theory which exploits the principle of optimality.

Many optimal control problems are solved completely in the body of the text. Furthermore, all of the exercise problems which appear at the ends of the chapters are sketched in the appendix.

The book also covers some material that is not usually found in optimal control text books, namely, optimal control problems with non-scalar-valued performance criteria (with applications to optimal filtering) and Lukes’ method of approximatively-optimal control design.

Furthermore, a short introduction to differential game theory is given. This leads to the Nash-Pontryagin Minimax Principle and to the Hamilton-Jacobi-Nash theory. The reason for including this topic lies in the important connection between the differential game theory and the H-control theory for the design of robust controllers.

Review

From the reviews:

"The book is based on the lecture material for a one-semester senior-year undergraduate or first-year graduate course in optimal control given by the author at the Swiss federal Institute of Technology (ETH Zürich) for more than twenty years. ... The book contains a variety of optimal control problems, many of which completely solved in details in the body of the text. Additional problems are given as exercises together with a sketch of the solutions." (Riccardo De Arcangelis, Zentralblatt MATH, Vol. 1121 (23), 2007)

“This 144-page book offers a concise introduction to optimal control theory and differential games, from the minimum principle (MP) to Hamilton-Jacobi-Bellman (HJB) theory. ... The style of the book is simplistic, sacrificing rigor for accessibility, which is appropriate for the intended readership. ... This is a good, concise book on optimal control and differential games that can easily be adapted as a textbook for an introductory course on the subject either at the senior undergraduate level or as a first-year graduate-level course.” (Panagiotis Tsiotras, IEEE Control Systems Magazine, Vol. 31, October, 2011)

Edition details

• Publisher: Springer
• Publication date: 2007
• ISBN 10: 3540694374
• ISBN 13: 9783540694373
• Binding: Paperback
• Language: English
• Number of pages: 143