Optimal Syntheses for Control Systems on 2-D Manifolds [Paperback]

This book is devoted to optimal syntheses in control theory and focuses on minimum time on 2-D manifolds. The text outlines examples of applicability, introduces geometric methods in control theory, and analyzes single input systems on 2-D manifolds including classifications of optimal syntheses and feedbacks, their singularities, extremals projection and minimum time singularities. Various extensions and applications are also illustrated.

Introduction.- Geometric Control.- Time Optimal Synthesis for 2-D Systems.- Generic Properties of the Minimum Time Function.- Extremal Synthesis.- Projection Singularities.- A. Some Technical Proofs of Chapter 2.- B. Bidimensional Sources.- References.- Index.

From the reviews:

This book provides an excellent illustration of concepts and methods of geometric optimal control at work. & This book is a welcome addition to a number of texts that treat the mathematical aspects of control theory from a geometric point of view & . accessible to the advanced, mathematically inclined graduate student and rewarding in their results. They provide plentiful and excellent material for a mathematically oriented graduate course on the topic & . (Heinz Schaettler, SIAM Reviews, Vol. 47 (3), 2005)

This monograph is the first devoted to optimal syntheses in control theory and focuses on minimum time on 2-D manifolds. The first chapter outlines book results and examples of applicability. Then a quick introduction to geometric methods in control theory is provided. The following chapters contain a deep analysis of single input systems on 2-D manifolds including classifications of optimal syntheses and feedbacks, their singularities, extremals projection and minimum time singularities. Various extensions and applications are also illustrated. The volume is suitable for a graduate Level one-semester course ol³"