Gathering the most important and promising results in subfields of nonlinear control theory;previously available only in journals;this comprehensive volume presents the state of the art in geometric methods, their applications in optimal control, and feedback transformations. Shows how geometric control theory draws from other mathematical fields to create its own powerful tools! Elucidating complex material and providing new directions for future research, Geometry of Feedback and Optimal Control discusses the latest applications, illustrating links between topics such as the Pontryagin Maximum Principle, differential geometric and symplectic methods, and the structure of reachable sets furnishes the most recent problems, including feedback stabilization, classification, and invariants covers the optimality of trajectories using the Maslov index delineates the role of singularity theory in stability theory and feedback equivalence explores singularities of systems, reachable sets, and stabilizing and optimal controls and much more! Supplemented with over 1200 references, equations, and drawings, this readily accessible resource is excellent for pure and applied mathematicians, analysts, and applied geometers specializing in control theory, differential equations, calculus of variations, differential geometry, and singularity theory, and graduate-level students in these disciplines.