Dynamical Systems and Microphysics : Control Theory and Mechanics : 3rd International Seminar on Mathematical Theory of Dynamical Systems and Microphysics : Papers

Dynamical Systems and Microphysics: Control Theory and Mechanics contains the proceedings of the Third International Seminar on Mathematical Theory of Dynamical Systems and Microphysics held in Udine, Italy, on September 4-9, 1983. The papers explore the mechanics and optimal control of dynamical systems and cover topics ranging from complete controllability and stability to feedback control in general relativity; adaptive control for uncertain dynamical systems; geometry of canonical transformations; and homogeneity in mechanics. This book is comprised of 14 chapters and begins by discussing the relationship between complete controllability and Poisson stabilizability in relation to to Liapounov stabilizability. The next chapter looks at the conditions that must be met in order to control a dynamical system in an optimal fashion. The theory of optimal feedback control is used as an approach to the dynamics of a mass point in general relativity. The theory of reachability with feedback control is also used as an approach to geometrical optics in the frame of general relativity. The final chapter describes a system theoretic framework for the study of Hamiltonian systems with external forces. This monograph is intended primarily for researchers and graduate students in theoretical physics, mechanics, control and system theory, and mathematics. It may also be read profitably by philosophers of science and, to some extent, by those who have a keen interest in basic questions of contemporary mechanics and physics and who possess some background in the physical and mathematical sciences. Content: Academic Press Rapid Manuscript Reproduction , Page ii Front Matter , Page iii Copyright , Page iv Contributors , Pages vii-viii Preface , Pages ix-x COMPLETE CONTROLLABILITY AND STABILIZABILITY , Pages 1-11 , Andrea Bacciotti OPTIMALITY WITH FEEDBACK CONTROL IN GENERAL RELATIVITY , Pages 13-43 , A. Blaquière REACHABILITY WITH FEEDBACK CONTROL IN GENERAL RELATIVITY , Pages 45-90 , A. Blaquière, M. Pauchard ADAPTIVE CONTROL FOR UNCERTAIN DYNAMICAL SYSTEMS , Pages 91-158 , M. Corless, G. Leitmann RETARDED POTENTIALS AND ASYMPTOTIC BEHAVIOR IN NON-HAMILTONIAN SYSTEMS , Pages 159-181 , Francis Fer GLOBAL REDUCTION OF A DYNAMICAL SYSTEM ON A FOLIATED MANIFOLD AND “CONTROLLED PROJECTABILITY” , Pages 183-205 , Ida Cattaneo Gasparini EVOLUTION EQUATIONS OF ALGEBRAIC FUNCTIONALS , Pages 207-220 , M. GINOCCHIO, M. IRAC-ASTAUD EXACT LINEARIZATION TECHNIQUES OF NONLINEAR SYSTEMS , Pages 221-241 , A. Isidori ON LOCAL CONTROLLABILITY OF NON-LINEAR SYSTEMS , Pages 243-286 , H.W. Knobloch, K. Wagner GEOMETRY OF THE CANONICAL TRANSFORMATIONS , Pages 287-327 , André Lichnerowicz SOME ASPECTS OF HOMOGENEITY IN MECHANICS , Pages 329-340 , L. LOSCO ON THE DEFINITION OF FORCES IN CONTINUUM MECHANICS , Pages 341-357 , Reuven Segev CONTROL OF STATIC MECHANICAL SYSTEMS , Pages 359-377 , W.M. Tulczyjew SYSTEM THEORETIC PROPERTIES OF HAMILTONIAN SYSTEMS WITH EXTERNAL FORCES , Pages 379-400 , A.J. van der Schaft Index , Pages 401-403