Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.

Autorentext

In addition to having served (1991 - 2001) as Chargé de Recherche at CNRS, and as, now, Directeur de Recherche at INRIA, Bernard Brogliato is an Associate Editor for Automatica (since 2001) a reviewer for Mathematical Reviews and writes book reviews for ASME Applied Mechanics Reviews. He has served on the organising and other committees of various European and international conferences sponsored by an assortment of organizations, most prominently, the IEEE. He has been responsible for examining the PhD and Habilitation theses of 16 students and takes an active part in lecturing at summer schools in several European countries. Doctor Brogliato is the director of SICONOS (a European project concerned with Modelling, Simulation and Control of Nonsmooth Dynamical Systems) which carries funding of EUR2 million.

Klappentext

PThis significantly enlarged and expanded second edition, focuses on nonsmooth finite dimensional mechanical systems, subject to unilateral constraints. It contains a complete overview of the main problems in the areas of mathematics, mechanics, stability and control, which are of interest in this field. The following topics are discussed in detail and are illustrated with examples: Short dynamics; Multiple impacts; Feedback control; Moreau's sweeping process; Complimentary formulations. With a comprehensive bibliography of over a thousand references, this book is an indispensable source of information on the subject treated. /PP/P TOC:Distributional Model of Impacts.- Approximating Problems.- Variation Principles.- Two Bodies Colliding.- Multiconstraint Nonsmooth Dynamics.- Generalized Impacts.- Stability of Nonsmooth Dynamical Systems.- Feedback Control.- Appendices: Schwartz' Distributions; Measures and Integrals; Functions of Bounded Variation in Time; Elements of Convex |Analysis; Dissipative Systems

Zusammenfassung
Focuses on a class of nonsmooth hybrid dynamical systems, namely finite-dimensional mechanical systems subject to unilateral constraints. This book contains overview of the main problems in mathematics, mechanics, stability and control. It discusses such topics as: shock dynamics; multiple impacts; feedback control; and, Moreau's sweeping process.

Inhalt

Distributional Model of Impacts.- Approximating Problems.- Variation Principles.- Two Bodies Colliding.- Multiconstraint Nonsmooth Dynamics.- Generalized Impacts.- Stability of Nonsmooth Dynamical Systems.- Feedback Control.- Appendices: Schwartz' Distributions; Measures and Integrals; Functions of Bounded Variation in Time; Elements of Convex |Analysis; Dissipative Systems