Dynamical Systems and Microphysics

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.

Contenu

Contributors
Preface
Complete Controllability and Stability
Optimality with Feedback Control in General Relativity
Reachability with Feedback Control in General Relativity
Adaptive Control for Uncertain Dynamical Systems
Retarded Potentials and Asymptotic Behavior in Non-Hamiltonian Systems
Global Reduction of a Dynamical System on a Foliated Manifold and "Controlled Projectability"
Evolution Equations of Algebraic Functionals
Exact Linearization Techniques of Nonlinear Systems
On Local Controllablity of Nonlinear Systems
Geometry of the Canonical Transformations
Some Aspects of Homogeneity in Mechanics
On the Definition of Forces in Continuum Mechanics
Control of Static Mechanical Systems
System Theoretic Properties of Hamiltonian Systems with External Forces
Index