Hans P. Geering
Optimal Control with Engineering Applications
With 12 Figures
Hans P. Geering, Ph.D. Professor of Automatic Control and Mechatronics Measurement and Control Laboratory
Department of Mechanical and Process Engineering ETH Zurich Sonneggstrasse 3 CH-8092 Zurich, Switzerland
Library of CongressControl Number: 2007920933
ISBN 978-3-540-69437-3 Springer Berlin Heidelberg New York
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This book is based on the lecture material for a one-semester senior-year undergraduate or ﬁrst-year graduate course in optimal control which I have taught at the Swiss Federal Institute of Technology (ETH Zurich) for more than twenty years. The students taking this course are mostly students in mechanicalengineering and electrical engineering taking a major in control. But there also are students in computer science and mathematics taking this course for credit. The only prerequisites for this book are: The reader should be familiar with dynamics in general and with the state space description of dynamic systems in particular. Furthermore, the reader should have a fairly sound understanding ofdiﬀerential calculus. The text mainly covers the design of open-loop optimal controls with the help of Pontryagin’s Minimum Principle, the conversion of optimal open-loop to optimal closed-loop controls, and the direct design of optimal closed-loop optimal controls using the Hamilton-Jacobi-Bellman theory. In theses areas, the text also covers two special topics which are not usually found in textbooks: theextension of optimal control theory to matrix-valued performance criteria and Lukes’ method for the iterative design of approximatively optimal controllers. Furthermore, an introduction to the phantastic, but incredibly intricate ﬁeld of diﬀerential games is given. The only reason for doing this lies in the fact that the diﬀerential games theory has (exactly) one simple application, namely the LQdiﬀerential game. It can be solved completely and it has a very attractive connection to the H∞ method for the design of robust linear time-invariant controllers for linear time-invariant plants. — This route is the easiest entry into H∞ theory. And I believe that every student majoring in control should become an expert in H∞ control design, too. The book contains a rather large variety ofoptimal control problems. Many of these problems are solved completely and in detail in the body of the text. Additional problems are given as exercises at the end of the chapters. The solutions to all of these exercises are sketched in the Solution section at the end of the book.
First, my thanks go to Michael Athans for elucidating me on the background of...