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Introduction to Geometric Control
This text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory. The concise presentation provides an accessible treatment of the subject for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as to experts in classic control theory for whom geometric methods may be introduced. Theory is accompanied by characteristic examples such as stopping a train, motion of mobile robot, Euler elasticae, Dido's problem, and rolling of the sphere on the plane. Quick foundations to some recent topics of interest like control on Lie groups and sub-Riemannian geometry ...
Control Theory from the Geometric Viewpoint
This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is com pletely determined by the initial conditions. Moreover, t...
Elements of Neurogeometry
This book describes several mathematical models of the primary visual cortex, referring them to a vast ensemble of experimental data and putting forward an original geometrical model for its functional architecture, that is, the highly specific organization of its neural connections. The book spells out the geometrical algorithms implemented by this functional architecture, or put another way, the “neurogeometry” immanent in visual perception. Focusing on the neural origins of our spatial representations, it demonstrates three things: firstly, the way the visual neurons filter the optical signal is closely related to a wavelet analysis; secondly, the contact structure of the 1-jets of th...
Mathematical Image Processing
The contributions appearing in this volume are a snapshot of the different topics that were discussed during the Second Conference "Mathematics and Image Processing” held at the University of Orléans in 2010. They mainly concern, image reconstruction, texture extraction and image classification and involve a variety of different methods and applications. Therefore it was impossible to split the papers into generic groups which is why they are presented in alphabetic order. However they mainly concern: texture analysis (5 papers) with different techniques (variational analysis, wavelet and morphological component analysis, fractional Brownian fields), geometrical methods (2 papers ) for restoration and invariant feature detection, classification (with multifractal analysis), neurosciences imaging and analysis of Multi-Valued Images.
Geometric Science of Information
This book constitutes the refereed proceedings of the Third International Conference on Geometric Science of Information, GSI 2017, held in Paris, France, in November 2017. The 101 full papers presented were carefully reviewed and selected from 113 submissions and are organized into the following subjects: statistics on non-linear data; shape space; optimal transport and applications: image processing; optimal transport and applications: signal processing; statistical manifold and hessian information geometry; monotone embedding in information geometry; information structure in neuroscience; geometric robotics and tracking; geometric mechanics and robotics; stochastic geometric mechanics and Lie group thermodynamics; probability on Riemannian manifolds; divergence geometry; non-parametric information geometry; optimization on manifold; computational information geometry; probability density estimation; session geometry of tensor-valued data; geodesic methods with constraints; applications of distance geometry.
A Comprehensive Introduction to Sub-Riemannian Geometry
Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.
Neuromathematics of Vision
This book is devoted to the study of the functional architecture of the visual cortex. Its geometrical structure is the differential geometry of the connectivity between neural cells. This connectivity is building and shaping the hidden brain structures underlying visual perception. The story of the problem runs over the last 30 years, since the discovery of Hubel and Wiesel of the modular structure of the primary visual cortex, and slowly cams towards a theoretical understanding of the experimental data on what we now know as functional architecture of the primary visual cortex. Experimental data comes from several domains: neurophysiology, phenomenology of perception and neurocognitive ima...
Control and Nonlinearity
This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics. The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations.
Mathematical Reviews
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