Geometric Methods For Nonparametric Modeling Of Dynamical Systems

Geometric Methods in System Theory In automatic control there are a large number of applications of a fairly simple type for which the motion of the state variables is not free to evolve in a vector space but rather must satisfy some constraints. Examples are numerous; in a switched, lossless electrical network energy is conserved and the state evolves on an ellipsoid surface defined by x'Qx equals a constant; in the control of finite state, continuous time, Markov processes the state evolves on the set x'x = 1, xi ~ O. The control of rigid body motions and trajectory control leads to problems of this type. There has been under way now for some time an effort to build up enough control theory to enable one to treat these problems in a more or less routine way. It is important to emphasise that the ordinary vector space-linear theory often gives the wrong insight and thus should not be relied upon.

A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.

The sharp analyses in this paper enable us to compare the performance of our method with other phase recovery schemes. Finally, the convergence analysis of the iterative algorithms are done by a geometric approach to dynamical systems. By analyzing the movements from iteration to iteration, we provide a general tool that can show global convergence for many two dimensional dynamical systems. We hope this can shed light on convergence analysis for general dynamical systems.

This volume contains the invited papers presented at the 9th International Conference "Dynamical Systems — Theory and Applications" held in Lódz, Poland, December 17-20, 2007, dealing with nonlinear dynamical systems. The conference brought together a large group of outstanding scientists and engineers, who deal with various problems of dynamics encountered both in engineering and in daily life. Topics covered include, among others, bifurcations and chaos in mechanical systems; control in dynamical systems; asymptotic methods in nonlinear dynamics; stability of dynamical systems; lumped and continuous systems vibrations; original numerical methods of vibration analysis; and man-machine interactions. Thus, the reader is given an overview of the most recent developments of dynamical systems and can follow the newest trends in this field of science. This book will be of interest to to pure and applied scientists working in the field of nonlinear dynamics.

Describes computational methods for parametric and nonparametric modeling of stochastic dynamics. Aimed at graduate students, and suitable for self-study.

This book gathers selected contributions presented at the INdAM Workshop “DREAMS”, held in Rome, Italy on January 22−26, 2018. Addressing cutting-edge research topics and advances in computer aided geometric design and isogeometric analysis, it covers distinguishing curve/surface constructions and spline models, with a special focus on emerging adaptive spline constructions, fundamental spline theory and related algorithms, as well as various aspects of isogeometric methods, e.g. efficient quadrature rules and spectral analysis for isogeometric B-spline discretizations. Applications in finite element and boundary element methods are also discussed. Given its scope, the book will be of interest to both researchers and graduate students working in these areas.

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.