Related papers: A short introduction to geometric control theory
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
This primer is an introduction to Conformal Field Theory in $D\geq3$. It is designed to introduce the reader to many of the important foundational concepts and methods in CFT. In it, pig picture ideas are prioritized over technical details,…
This paper proposes an adaptive modular geometric control framework for robotic manipulators. The proposed methodology decomposes the overall manipulator dynamics into individual modules, enabling the design of local geometric control laws…
In this paper we give a new formulation of an abstract control problem in terms of a Grushin problem, so that we will reformulate all notions of controllability, observability and stability in a new form that gives readers an easy…
These brief lecture notes are intended mainly for undergraduate students in engineering or physics or mathematics who have met or will soon be meeting the Dirac delta function and some other objects related to it. These students might have…
We give a rather informal introduction to the theory of mixed Hodge modules for young mathematicians.
The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…
The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.
This paper gives a short introduction into the metric theory of spaces with dilations.
In this note, we develop the first-order theory of optimal control problems with box constraints on the control. We emphasize the precise modification of Pontryagin's maximum principle when the admissible control set is compact, the…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
While reinforcement learning has made great improvements, state-of-the-art algorithms can still struggle with seemingly simple set-point feedback control problems. One reason for this is that the learned controller may not be able to excite…
First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…
This paper presents a new technique for the design of approximate reasoning based controllers for dynamic physical systems with interacting goals. In this approach, goals are achieved based on a hierarchy defined by a control knowledge base…
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
The goal of this book is to provide an introduction to the mathematical theory of Kinetically constrained models developed in the last twenty years, intended for both mathematicians and physicists.
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
We describe a particular control method for a system controlled by several actuators with the same control constants. We show under certain assumptions that the control constants for the whole system can be obtained immediately from the…
This short note is a conceptual prologue to the series of articles devoted to the analysis of interrelations between the representation theory (especially, its inverse problems) and the control and games theory.