scholarly journals Optimization of a control law to synchronize first-order dynamical systems on Riemannian manifolds by a transverse component

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Adolfo Damiano Cafaro ◽  
Simone Fiori
Keyword(s):  
Dynamical Systems ◽  
Riemannian Manifolds ◽  
Transverse Component ◽  
Point Of View ◽  
Control Law ◽  
Theoretical Point ◽  
Control Effort ◽  
First Order ◽  
Linear Control Theory ◽  
Non Linear

<p style='text-indent:20px;'>The present paper builds on the previous contribution by the second author, S. Fiori, <i>Synchronization of first-order autonomous oscillators on Riemannian manifolds</i>, Discrete and Continuous Dynamical Systems – Series B, Vol. 24, No. 4, pp. 1725 – 1741, April 2019. The aim of the present paper is to optimize a previously-developed control law to achieve synchronization of first-order non-linear oscillators whose state evolves on a Riemannian manifold. The optimization of such control law has been achieved by introducing a transverse control field, which guarantees reduced control effort without affecting the synchronization speed of the oscillators. The developed non-linear control theory has been analyzed from a theoretical point of view as well as through a comprehensive series of numerical experiments.</p>

scholarly journals The Road to Modern Logic—An Interpretation

2001 ◽  
Vol 7 (4) ◽  
pp. 441-484 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Order Logic ◽  
Point Of View ◽  
First Order Logic ◽  
Theoretical Point ◽  
Primary Role ◽  
Philosophical Discussion ◽  
Modern Logic ◽  
Core System ◽  
First Order ◽  
The Road

AbstractThis paper aims to outline an analysis and interpretation of the process that led to First-Order Logic and its consolidation as a core system of modern logic. We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order Logic. On this basis, we advance the thesis that a certain historical tradition was essential to the emergence of modern logic; this traditional context is analyzed as consisting in some guiding principles and, particularly, a set of exemplars (i.e., paradigmatic instances). Then, we proceed to interpret the historical course of development reviewed in section 1, which can broadly be described as a two-phased movement of expansion and then restriction of the scope of logical theory. We shall try to pinpoint ambivalencies in the process, and the main motives for subsequent changes. Among the latter, one may emphasize the spirit of modern axiomatics, the situation of foundational insecurity in the 1920s, the resulting desire to find systems well-behaved from a proof-theoretical point of view, and the metatheoretical results of the 1930s. Not surprisingly, the mathematical and, more specifically, the foundational context in which First-Order Logic matured will be seen to have played a primary role in its shaping.Mathematical logic is what logic, through twenty-five centuries and a few transformations, has become today. (Jean van Heijenoort)

scholarly journals Family of controllers based on sector non-linear functions: an application for first-order dynamical systems

2020 ◽  
Vol 14 (10) ◽  
pp. 1387-1392
Author(s):  
Marlen Meza-Sánchez ◽  
Maria del Carmen Rodríguez-Liñán ◽  
Eddie Clemente
Keyword(s):  
Dynamical Systems ◽  
Linear Functions ◽  
First Order ◽  
Non Linear

Design. Create. Learn. Repeat.

2021 ◽  
Author(s):  
Manuel Reventós ◽  
Jaume Guàrdia
Keyword(s):  
Design Process ◽  
User Experience ◽  
Creative Process ◽  
Point Of View ◽  
Theoretical Point ◽  
Technological Tools ◽  
Non Linear ◽  
Complex Forms ◽  
First Time

<p>The designing process of a footbridge is complex, many variables must be considered that are non-linear and feedback on each other. The creative process is iterative, approximating and depending on the conditions of the environment. In this process is very important the intuition of the designer, or expert, which leads the result in one or another direction.</p><p>But how is born this intuition? How is it created? It's hard to narrow down, it's like trying to teach a child how to ride a bike. You have to pedal, for the first time you fall, but after a few hits on the ground you start to ride alone. Intuition is learned through experience and not with books, you learn designing, building, creating.</p><p>Every new project we face is fed with our previous experiences. In this article we explain our design process through our most recent projects, both successful and problematic.</p><p>In this moment the technological tools have reached to us the most complex forms. We must think about if this should define our way of designing and the footbridges we make. Technology and technique are the tools we have to define forms and materials. But there are other aspects such as the location, its itinerary of the path, the accesses, how it relates to the environment, the user experience and the constructive details, that are elements which define the solution and it cannot be analysed from a theoretical point of view. Each situation is unique and is where the experience of the expert cannot be replaced.</p>

scholarly journals A SPECTRAL APPROACH TO YANG-MILLS THEORY

2002 ◽  
Vol 17 (06n07) ◽  
pp. 926-935
Author(s):  
GIAMPIERO ESPOSITO
Keyword(s):  
Riemannian Manifolds ◽  
Differential Operators ◽  
Coulomb Gauge ◽  
Point Of View ◽  
Order Differential Operator ◽  
Matrix Elements ◽  
Four Dimensions ◽  
Yang Mills ◽  
First Order ◽  
Pseudo Differential Operators

Yang–Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator [Formula: see text] built from the Laplacian and from a first-order differential operator. The operator [Formula: see text] is studied from the point of view of spectral theory of pseudo-differential operators on compact Riemannian manifolds, both when self-adjointness holds and when it is not fulfilled. In both cases, well-defined matrix elements of [Formula: see text] are evaluated as a first step towards the more difficult problems of quantized Yang–Mills theory.

scholarly journals PRODUCT-FORM IN G-NETWORKS

2016 ◽  
Vol 30 (3) ◽  
pp. 345-360 ◽  
Author(s):  
Andrea Marin
Keyword(s):  
Stochastic Modeling ◽  
Queueing Networks ◽  
Equilibrium Distribution ◽  
Queueing Network ◽  
Point Of View ◽  
Product Form ◽  
Theoretical Point ◽  
Non Linear ◽  
Modular Analysis ◽  
Product Forms

The introduction of the class of queueing networks called G-networks by Gelenbe has been a breakthrough in the field of stochastic modeling since it has largely expanded the class of models which are analytically or numerically tractable. From a theoretical point of view, the introduction of the G-networks has lead to very important considerations: first, a product-form queueing network may have non-linear traffic equations; secondly, we can have a product-form equilibrium distribution even if the customer routing is defined in such a way that more than two queues can change their states at the same time epoch. In this work, we review some of the classes of product-forms introduced for the analysis of the G-networks with special attention to these two aspects. We propose a methodology that, coherently with the product-form result, allows for a modular analysis of the G-queues to derive the equilibrium distribution of the network.

Time-Dependent Thermal Convection

1983 ◽  
Vol 5 (2) ◽  
pp. 173-175 ◽  
Author(s):  
J. M. Lopez ◽  
J. O. Murphy
Keyword(s):  
Thermal Convection ◽  
Point Of View ◽  
Time Dependent ◽  
Theoretical Point ◽  
Temporal Behaviour ◽  
Benard Convection ◽  
Non Linear ◽  
Linear Behaviour ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The temporal behaviour of Rayleigh-Benard convection has attracted considerable attention in recent years, both from an experimental and theoretical point of view. Experiments (eg. Gollub and Benson 1980) have demonstrated a complicated array of non-linear behaviour, as well as the need for a model which will at least qualitatively describe what is observed.

FEASIBILITY PROOF FOR ARBITRARILY TIGHT PHASE EQUALIZATION

1991 ◽  
Vol 01 (01) ◽  
pp. 1-18 ◽  
Author(s):  
ANTON KUMMERT ◽  
ALFRED FETTWEIS
Keyword(s):  
Continuous Time ◽  
Mathematical Proof ◽  
Point Of View ◽  
Frequency Interval ◽  
Theoretical Point ◽  
Linear Phase ◽  
Finite Frequency ◽  
First Order ◽  
Time Linear ◽  
Equalization Problem

In this paper, the phase equalization problem for continuous-time us well as for discrete-time linear systems is considered from a theoretical point of view. The purpose is thus not to present an efficient algorithm for solving this problem in practice, but to offer a mathematical proof that an arbitrarily tight approximation of the linear phase behavior in any given finite frequency interval is always feasible. In a first step it is shown that the problem can be reduced to the equalization of the phase of a real first-order all-pass section. This simplified problem is investigated in Sec. 4.2 of the paper.

scholarly journals On the origin and development of some notions of entropy

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Francisco Balibrea
Keyword(s):  
Applied Sciences ◽  
Dynamical Systems ◽  
Topological Entropy ◽  
Discrete Dynamical Systems ◽  
Point Of View ◽  
Topological Dynamics ◽  
Theoretical Point ◽  
Compact Metric Space ◽  
Continuous Maps ◽  
And Control

AbstractDiscrete dynamical systems are given by the pair (X, f ) where X is a compact metric space and f : X → X a continuous maps. During years, a long list of results have appeared to precise and understand what is the complexity of the systems. Among them, one of the most popular is that of topological entropy. In modern applications other conditions on X and f have been considered. For example X can be non-compact or f can be discontinuous (only in a finite number of points and with bounded jumps on the values of f or even non-bounded jumps). Such systems are interesting from theoretical point of view in Topological Dynamics and appear frequently in applied sciences such as Electronics and Control Theory. In this paper we are dealing mainly with the original ideas of entropy in Thermodinamics and their evolution until the appearing in the twenty century of the notions of Shannon and Kolmogorov-Sinai entropies and the subsequent topological entropy. In turn such notions have to evolve to other recent situations where it is necessary to give some extended versions of them adapted to the new problems.

scholarly journals On Epistemics in Expected Free Energy for Linear Gaussian State Space Models

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1565
Author(s):  
Magnus T. Koudahl ◽  
Wouter M. Kouw ◽  
Bert de Vries
Keyword(s):  
Free Energy ◽  
Dynamical Systems ◽  
Intelligent Systems ◽  
Point Of View ◽  
Gaussian State ◽  
Theoretical Point ◽  
Transition Matrices ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Depth Analysis

Active Inference (AIF) is a framework that can be used both to describe information processing in naturally intelligent systems, such as the human brain, and to design synthetic intelligent systems (agents). In this paper we show that Expected Free Energy (EFE) minimisation, a core feature of the framework, does not lead to purposeful explorative behaviour in linear Gaussian dynamical systems. We provide a simple proof that, due to the specific construction used for the EFE, the terms responsible for the exploratory (epistemic) drive become constant in the case of linear Gaussian systems. This renders AIF equivalent to KL control. From a theoretical point of view this is an interesting result since it is generally assumed that EFE minimisation will always introduce an exploratory drive in AIF agents. While the full EFE objective does not lead to exploration in linear Gaussian dynamical systems, the principles of its construction can still be used to design objectives that include an epistemic drive. We provide an in-depth analysis of the mechanics behind the epistemic drive of AIF agents and show how to design objectives for linear Gaussian dynamical systems that do include an epistemic drive. Concretely, we show that focusing solely on epistemics and dispensing with goal-directed terms leads to a form of maximum entropy exploration that is heavily dependent on the type of control signals driving the system. Additive controls do not permit such exploration. From a practical point of view this is an important result since linear Gaussian dynamical systems with additive controls are an extensively used model class, encompassing for instance Linear Quadratic Gaussian controllers. On the other hand, linear Gaussian dynamical systems driven by multiplicative controls such as switching transition matrices do permit an exploratory drive.

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