This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints.

This book explores some of the connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints. The synthesis of the topic is appropriate as there is a particularly rich connection between mechanics and nonlinear control theory. The book provides a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material not available in other recent texts and monographs. The book will be of particular benefit to graduate students who wish to learn this subject and researchers in the area who want to enhance their techniques.

Includes supplementary material: sn.pub/extras

Klappentext

Nonholonomic Mechanics and Control develops the rich connections between control theory and geometric mechanics. Control theory is linked with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations and especially with the theory of nonholonomic mechanics (mechanical systems subject to motion constraints). Both controllability and optimal control are treated, including the Pontryagin maximum principle. In addition, the stability, control, and stabilization of mechanical systems are discussed. In particular, these items are considered for nonholonomic systems. The aim of the book is to provide a unified treatment of nonlinear control theory and constrained mechanical systems, incorporating material that has not yet made its way into texts and monographs. Detailed illustrations and exercises are included throughout the text.

This book is intended for graduate and advance undergraduate students in mathematics, physics and engineering who wish to learn this subject and for researchers in the area who want to enhance their techniques.

Inhalt
Mathematical Preliminaries.- Basic Concepts in Geometric Mechanics.- to Aspects of Geometric Control Theory.- Nonholonomic Mechanics.- Control of Mechanical and Nonholonomic Systems.- Optimal Control.- Stability of Nonholonomic Systems.- Energy-Based Methods for Stabilization Controlled Lagrangian Systems.