Geometric Control of Mechanical Systems

Our goal in this book is to explore some of the connections between control theory and geometric mechanics; that is, we link control theory with a g- metric view of classical mechanics in both its Lagrangian and Hamiltonian formulations and in particular with the theory of mechanical systems s- ject to motion constraints. This synthesis of topics is appropriate, since there is a particularly rich connection between mechanics and nonlinear control theory. While an introduction to many important aspects of the mechanics of nonholonomically constrained systems may be found in such sources as the monograph of Neimark and Fufaev [1972], the geometric view as well as the control theory of such systems remains largely sc- tered through various research journals. Our aim is to provide a uni?ed treatment of nonlinear control theory and constrained mechanical systems that will incorporate material that has not yet made its way into texts and monographs. Mechanicshastraditionallydescribedthebehavioroffreeandinteracting particles and bodies, the interaction being described by potential forces. It encompasses the Lagrangian and Hamiltonian pictures and in its modern form relies heavily on the tools of di?erential geometry (see, for example, Abraham and Marsden [1978]and Arnold [1989]). From our own point of view,ourpapersBloch,Krishnaprasad,Marsden,andMurray[1996],Bloch and Crouch [1995], and Baillieul [1998] have been particularly in?uential in the formulations presented in this book. Control Theory and Nonholonomic Systems. Control theory is the theory of prescribing motion for dynamical systems rather than describing vi Preface their observed behavior.

by Madhu N. Belur (Editor), M. Kanat Camlibel (Editor), Paolo Rapisarda (Editor), Jacquelien M.A. Scherpen (Editor)

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.

Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability and bifurcation, and the study of specific rigid, fluid, plasma and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous specific applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and up-to-date techniques, all of which makes it accessible to a wide variety of readers, expecially senior undergraduate and graduate students in mathematics, physics and engineering. For this second edition, the text has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available on-line.

Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability and bifurcation, and the study of specific rigid, fluid, plasma and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous specific applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and up-to-date techniques, all of which makes it accessible to a wide variety of readers, expecially senior undergraduate and graduate students in mathematics, physics and engineering. For this second edition, the text has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available on-line.

Editors: van de Wouw, Nathan, Lefeber, Erjen, Lopez Arteaga, Ines (Eds.)
Addresses important open problems in control of nonlinear systems
Inspires ideas for new research by providing informative contributions from an authoritative group of international experts
Presents a unique overview of important developments in nonlinear systems reflecting the work of Professor Henk Nijmeijer