Related papers: A short introduction to geometric control theory
A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.
This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it…
This is a short introduction to quantum computers, quantum algorithms and quantum error correcting codes. Familiarity with the principles of quantum theory is assumed. Emphasis is put on a concise presentation of the principles avoiding…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished circle. This provides a completely…
This paper reviews the design of regulation loops for power converters. Power converter control being a vast domain, it does not aim to be exhaustive. The objective is to give a rapid overview of the main synthesis methods in both…
Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle…
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
This paper is devoted to a study of linear, differential and topological classifications for linear controlled systems governed by ordinary differential equations. The necessary and sufficient conditions for the linear and topological…
This primer is intended as an introduction to differential forms, a central object in modern mathematical physics, for scientists and engineers.
These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.
These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
In this article we present an elementary introduction to the theory of minimal surfaces in Euclidean spaces $\mathbb R^n$ for $n\ge 3$ by using only elementary calculus of functions of several variables at the level of a typical second-year…
These notes, based on a graduate course I gave at Hamburg University in 2003, are intended to students having basic knowledges of differential geometry. Their main purpose is to provide a quick and accessible introduction to different…
This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of…
The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic…
The purpose of this sophomore-level textbook is twofold: to introduce the student to classical electrodynamics and, at the same time, explain in simple terms the quantum theory of conducting substances (in particular, the solid ones). The…
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…