Beschreibung:
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 semester course on optimal syntheses theory for a graduate course to mathematicians or engieneers with solid mathematical background. TOC:Introduction.- 1. Geometric Control.- 2. Time Optimal Synthesis for 2-D Systems.- 3. Generic Properties of the Minimum Time Function.- 4. Extremal Synthesis.- 5. Projection Singularities.- A. Some Technical Proofs of Chapter 2.- B. Bidimensional Sources.- References.- Index