Optimal Control with Engineering Applications
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Beschreibung
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.
In this book, the reader is introduced to a variety of problem statements in classical optimal control, in optimal control problems with non-scalar performance criteria, and in optimal estimation and filtering. The optimal control theory is based on rather basic methods in the calculus of variation, in particular on the Lagrange multiplier methods. The theory is explained in a very transparent way.
Many engineering optimal control problems are solved completely. Each chapter contains a small collection of additional statements of optimal control problems. Their solutions are sketched in the appendix.
Hands-on experience in using the theory with a variety of examples Didactically optimized way of exposition of the calculus of variation Easy to read for non-mathematicians, too Rather large number of completely solved real-world optimal control problems Includes non-scalar performance criteria and optimal filtering Includes supplementary material: sn.pub/extras
Autor*in
Hans P. Geering
Themen in »Optimal Control with Engineering Applications«
Calculus of Variations Optimal control Pontryagin's minimum principle calculus calculus of variation game theory optimal filtering optimization sketch
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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)
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