Introduction to Geometric Control

This text is a comprehensive introduction to geometric control theory, suitable for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as experts in classic control theory. It covers controllability and optimal control problems for nonlinear nonholonomic systems on smooth manifolds, including Lie groups. The applications-oriented approach discusses core subjects and encourages readers to solve related challenges independently. Selected sections provide exercises to assist in deeper understanding of the material.

Format: Paperback / softback
Length: 162 pages
Publication date: 24 June 2022
Publisher: Springer International Publishing AG

This text is an enhanced, English version of the Russian edition, published in early 2021, and is appropriate for an introductory course in geometric control theory. The concise presentation provides an accessible treatment of the subject for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as to experts in classic control theory for whom geometric methods may be introduced. Theory is accompanied by characteristic examples such as stopping a train, motion of a mobile robot, Euler elasticae, Dido's problem, and rolling of the sphere on the plane. Quick foundations to some recent topics of interest, like control on Lie groups and sub-Riemannian geometry, are included. Prerequisites include only a basic knowledge of calculus, linear algebra, and ODEs; preliminary knowledge of control theory is not assumed. The applications problems-oriented approach discusses core subjects and encourages the reader to solve related challenges independently. Highly-motivated readers can acquire working knowledge of geometric control techniques and progress to studying control problems and more comprehensive books on their own. Selected sections provide exercises to assist in deeper understanding of the material.

Controllability and optimal control problems are considered for nonlinear nonholonomic systems on smooth manifolds, in particular, on Lie groups. For the controllability problem, the following questions are considered: controllability of linear systems, local controllability of nonlinear systems, Nagano–Sussmann Orbit theorem, Rashevskii–Chow theorem theorem, Krener's theorem. For the optimal control problem, Filippov's theorem is stated, invariant formulation of Pontryagin maximum principle on manifolds is given, second-order optimality conditions are dis.

Weight: 285g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031020728
Edition number: 1st ed. 2022