Geometric Optimal Control

This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.

Comprehensive presentation of an up-to-date geometric approach to optimal control, both necessary and sufficient conditions, which has not been done in a book form before Rigorous presentation, written in a easy tutorial style accessible to non-experts and advanced undergraduate and graduate students Palette of fully and in detail worked out, well illustrated, nontrivial examples which are only available in the research literature Includes supplementary material: sn.pub/extras

Autorentext

Heinz Schättler is a Professor of Electrical and Systems Engineering at Washington University in St. Louis. He holds a Master's degree in Mathematics from the University of Würzburg in Germany and a Ph.D. in Mathematics from Rutgers University. His main research area is optimal control theory where he has published extensively on applications of methods and tools from optimal control and dynamical systems theory to problems motivated by real life applications. Besides the medical topics that are the focus of this text, these include electric power systems as well as models in economics, physics and electronics. Urszula Ledzewicz is a Distinguished Research Professor in the Department of Mathematics and Statistics at Southern Illinois University Edwardsville. She specialized in optimal control theory at the University of Lodz, Poland, where she received a master's and doctorate in Applied Mathematics. Her research interests include optimal control and optimization, mathematicalmodeling and analysis of systems in biomedicine with special emphasis on mathematical models for cancer growth and treatments. She has been active in the field as an Associate Editor of numerous scientific journals focused on nonlinear analysis, dynamical systems and mathematical biosciences. The authors also have published the text Geometric Optimal Control - Theory, Methods and Examples (Springer, 2012) and were co-editors for Mathematical Methods and Models in Biomedicine (Springer, 2012).

Inhalt
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.