Geometric Optimal Control

Urszula Ledzewicz is a Distinguished Research Professor in the Department of Mathematics and Statistics at Southern Illinois University. Heinz Schaettler is an Associate Professor at Washington University.

• The Calculus of Variations: A Historical Perspective.- The Pontryagin Maximum Principle: From Necessary Conditions to the Construction of an Optimal Solution.- Reachable Sets of Linear Time-Invariant Systems: From Convex Sets to the Bang-Bang Theorem.- The High-Order Maximum Principle: From Approximations of Reachable Sets to High-Order Necessary Conditions for Optimality.- The Method of Characteristics: A Geometric Approach to Sufficient Conditions for a Local Minimum.- Synthesis of Optimal Controlled Trajectories: FromLocal to Global Solutions.- Control-Affine Systems in Low Dimensions: From Small-Time Reachable Sets to Time-Optimal Syntheses.- References.- Index.

From the reviews: "The monograph under review concerns finite-dimensional deterministic optimal control problems. ... The main body of the book is divided into seven chapters. ... The variety of fully solved examples that illustrate the theory makes this text a strong educational asset. The book is recommended as a comprehensive textbook for both advanced undergraduate and all levels of graduate courses on optimal control in mathematics and engineering." (Ovidiu Carja, zbMATH, Vol. 1276, 2014) "The book presents a comprehensive treatment of both necessary and sufficient conditions for optimal control using geometric approach ... . The book is of interest to senior and graduate students in engineering and mathematics, and scientists and engineers working in academic and industrial organizations. ... The book is a valuable addition to some of the recent books on this ever-green field of Optimal Control ... ." (D. Subbaram Naidu, Amazon.com, September, 2013) "Grown out of well-tested lecture notes, large parts of this volume are suitable as a comprehensive textbook at an advanced undergraduate or at the graduate level, either in mathematics or in engineering ... . this most readable text provides a rich and versatile resource which is suitable as a textbook in various settings, is a valuable reference for theory, and which provides a very large collection of model examples that are analyzed completely using state-of-the-art methods." (Matthias Kawski, Mathematical Reviews, February, 2013) "Schattler (electrical and systems engineering, Washington Univ.) and Ledzewicz (mathematics and statistics, Southern Illinois Univ.) use a geometric approach to present the theory of optimal control. ... authors have developed a general approach that can be applied to a wide variety of control problems. ... This book may be of interest to graduate students and researchers working in this area. Summing Up: Recommended. Graduate students and researchers/faculty." (B. Borchers, Choice, Vol. 50 (5), January, 2013)