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129 results on '"Emmanuel Moulay"'

1. Einstein-Rosen bridge from the minimal length

Author

Kimet Jusufi, Emmanuel Moulay, Jonas Mureika, and Ahmed Farag Ali

Subjects
Astrophysics, QB460-466, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We use a string T-duality corrected pair of regular black holes to construct an Einstein-Rosen (ER) bridge with the wormhole throat proportional to the zero-point (Planck) length. This may be a geometric realization of quantum entanglement for particle/antiparticle pairs. We point out that for an extreme mass configuration consisting of a black hole pair, one can have an ER bridge with a horizon area that coincides with the Bekenstein minimal area bound along with a wormhole mass proportional to the Planck mass. This could be related to gravitational self-completeness with quantum mechanical mass limits. We also discuss the ER bridge for sub-Planckian mass horizonless wormholes and show this admits a region of negative energy at the throat, which we posit to be related to a particle of negative mass generated by quantum fluctuations or the Casimir effect. We argue that Hawking radiation could be the best way for the geometric realization of quantum entanglement for particle/antiparticle pairs emitted by black holes. This sheds new light on the ER=EPR conjecture.

Published
2023
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2. Unitary symmetries in wormhole geometry and its thermodynamics

Author

Ahmed Farag Ali, Emmanuel Moulay, Kimet Jusufi, and Hassan Alshal

Subjects
Astrophysics, QB460-466, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract From a geometric point of view, we show that the unitary symmetries $${{\,\textrm{U}\,}}(1)$$ U ( 1 ) and $${{\,\textrm{SU}\,}}(2)$$ SU ( 2 ) stem fundamentally from Schwarzschild and Reissner–Nordström wormhole geometry through spacetime complexification. Then, we develop quantum tunneling which makes these wormholes traversable for particles. Finally, this leads to wormhole thermodynamics.

Published
2022
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3. Non-collapsing wave functions in an infinite universe

Author

Emmanuel Moulay

Subjects
Infinite universe, Wave function collapse, Cosmological principle, Physics, QC1-999
Abstract

The main goal of this article is to show that there exist wave functions which never collapse in an infinite universe. These are the quantum states of similar quantum systems evolving in similar observable universes.

Published
2014
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25. Robust Fixed-Time Stability: Application to Sliding-Mode Control

Author

Vincent Léchappé, Emmanuel Bernuau, Emmanuel Moulay, Franck Plestan, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Paris-Saclay Food and Bioproduct Engineering (SayFood), AgroParisTech-Université Paris-Saclay-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Sliding mode control, 020208 electrical & electronic engineering, Robust control, Scalar (physics), Fixed-time stability, 02 engineering and technology, Stability (probability), Computer Science Applications, Second order systems, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Fixed time, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Constant (mathematics), Mathematics
Abstract

International audience; This article deals with robust fixed-time stability and stabilization. First, new global robust fixed-time stability results are proposed for scalar systems by using constant and variable exponent coefficients. Then, they are applied to global robust fixed-time stabilization of a class of uncertain nonlinear second order systems by using sliding mode control. All the results are illustrated in simulation.

Published
2022

26. Differential Topology

Author

Wouter Jongeneel and Emmanuel Moulay

Abstract

In this chapter we discuss differentiable structures on topological manifolds. In particular, we discuss transversality, tubular neighbourhoods, index theory, the degree and the theorems by Poincaré and Hopf and Bobylev and Krasnosel’skiĭ.

Published
2023

27. General Topology

Author

Wouter Jongeneel and Emmanuel Moulay

Abstract

This chapter presents the main general topological tools, as used in later parts. In particular we highlight topological manifolds, homotopies and retractions.

Published
2023

28. Introduction

Author

Wouter Jongeneel and Emmanuel Moulay

Abstract

This first chapter puts forward the potential and arguably necessity of employing topological methods when studying nonlinear dynamical control systems. This potential is further emphasized by highlighting the historical development of Poincaré’s qualitative work until the 1980s. Furthermore, we introduce a running example and discuss related work and the contents of this monograph

Published
2023

30. Towards Accepting and Overcoming Topological Obstructions

Author

Wouter Jongeneel and Emmanuel Moulay

Abstract

This chapter briefly highlights how one might address the aforementioned topological obstructions. We discuss almost global stabilization, periodic time-varying feedback and the broadest and most successful framework for discontinuous feedback: hybrid control theory.

Published
2023

31. Unitary symmetries in wormhole geometry and its thermodynamics

Author

Ahmed Farag Ali, Emmanuel Moulay, Kimet Jusufi, and Hassan Alshal

Subjects
High Energy Physics - Theory, Quantum Physics, Physics and Astronomy (miscellaneous), High Energy Physics - Theory (hep-th), FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Quantum Physics (quant-ph), Engineering (miscellaneous), General Relativity and Quantum Cosmology
Abstract

From a geometric point of view, we show that the unitary symmetries $U(1)$ and $SU(2)$ stem fundamentally from Schwarzschild and Reissner-Nordstr\"om wormhole geometry through spacetime complexification. Then, we develop quantum tunneling which makes these wormholes traversable for particles. Finally, this leads to wormhole thermodynamics., Comment: 20 pages, revtex4, 1 figure, Published in European Physical Journal C

Published
2023
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32. Generalizations and Open Problems

Author

Wouter Jongeneel and Emmanuel Moulay

Abstract

This chapter concludes the monograph and provides a brief overview of generalizations, ongoing work and open problems. In particular, by means of periodic orbits we highlight analogous discrete-time theory. Moreover, we remark how to generalize the classical Poincaré–Hopf theorem and we highlight Morse–, Lusternik–Schnirelmann– and Conley (index) theory.

Published
2023

33. Topological Obstructions

Author

Wouter Jongeneel and Emmanuel Moulay

Abstract

Given the previous chapters on topology and dynamical system theory, we can now provide a consistent treatment of topological obstructions to stability and stabilization. In particular, we will see how the retraction theory from Sect. 2.2 and the index results due to Bobylev, Krasnosel’skiĭ and Zabreĭko from Sect. 3.5 cover most of the existing results, conceptually. The current chapter focuses on the obstructions themselves and the next chapter highlights potential solutions.

Published
2023

34. Dynamical Control Systems

Author

Wouter Jongeneel and Emmanuel Moulay

Abstract

In this chapter we define dynamical control systems over spaces previously discussed and we formalize concepts as touched upon in Chap. 3. We start by introducing continuous-time dynamical systems on manifolds and a variety of stability notions. Then, we highlight Lyapunov stability theory, in particular, converse results. We end by detailing continuous control systems and a few stabilization paradigms.

Published
2023

35. Algebraic Topology

Author

Wouter Jongeneel and Emmanuel Moulay

Abstract

In this chapter we briefly introduce important concepts from homology theory and we highlight how some results from Chap. 3 can be understood through the lens of algebraic topology. This chapter accumulates in showing that the Euler characteristic can be understood by means of CW complexes, homology or intersection theory.

Published
2023

41. Fixed-time stabilization of fuzzy neutral-type inertial neural networks with time-varying delay

Author

Qing Hui, Chaouki Aouiti, Emmanuel Moulay, Hediene Jallouli, Université de Carthage - University of Carthage, University of Nebraska [Lincoln], University of Nebraska System, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), and Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Inertial frame of reference, Artificial neural network, Dynamical systems theory, Logic, Feedback control, fuzzy neural networks, 02 engineering and technology, Inertial neural networks, Type (model theory), Fuzzy logic, time-varying delay, 020901 industrial engineering & automation, Artificial Intelligence, Control theory, Fixed time, fixed-time stability, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Stability theorem, Mathematics
Abstract

International audience; This paper addresses the problem of fixed-time stabilization for a class of fuzzy neutral-type inertial neural networks (FNTINNs) with time-varying delay. By using a novel fixed-time stability theorem for dynamical systems, two different feedback control laws are designed to ensure the fixed-time stabilization of FNTINNs with time-varying delay. The proposed theoretical results can lead to a better upper settling-time estimation compared to existing results. Finally, three simulation examples are provided to illustrate the validity of the proposed theoretical results.

Published
2021

42. Sliding mode control-based fixed-time stabilization and synchronization of inertial neural networks with time-varying delays

Author

Emmanuel Moulay, Chaouki Aouiti, Qing Hui, and Hediene Jallouli

Subjects
0209 industrial biotechnology, Polynomial, Inertial frame of reference, Artificial neural network, Computer science, Mode (statistics), 02 engineering and technology, Function (mathematics), Sliding mode control, Synchronization, 020901 industrial engineering & automation, Artificial Intelligence, Control theory, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Gravitational singularity, Software
Abstract

In this article, we are interested in the fixed-time stabilization (FTSt) and fixed-time synchronization (FTSy) of a class of inertial neural networks with time-varying and distributed delays. To obtain FTSt and FTSy, sliding mode controllers are developed based on sliding mode control techniques and by using sliding variables. Two polynomial feedback control laws are exploited to achieve the FTSt and the FTSy but they are singular. To get rid of the singularities, the saturation function is used into the design of the controllers and the almost FTSt and almost FTSy are proved. Finally, numerical examples are presented to show the effectiveness of the theoretical results.

Published
2021

45. Predictor-Based Control of LTI Remote Systems With Estimated Time-Varying Delays

Author

Emmanuel Moulay, Franck Plestan, Yang Deng, Vincent Léchappé, Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), École Centrale de Nantes (ECN), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
Control and Optimization, Computer science, Control (management), Signal, [SPI.AUTO]Engineering Sciences [physics]/Automatic, law.invention, Loop (topology), Control and Systems Engineering, Control theory, law, Finite time, Estimation, Remote control, Delay systems, Lyapunov methods
Abstract

International audience; This paper provides a practical control solution to remote control systems with unknown time-varying delays. An external signal which can be considered as a specific communication loop is added to estimate the unknown round-trip delay in finite time. Then the system is stabilized with the practical delay estimation technique and a predictor-based controller. The main results of this paper also provide an alternative way to design predictor-based controller for systems with known input and output time-varying delays. The theoretical results of this paper are illustrated by simulation results.

Published
2021

46. Semi‐Markov models of epidemics over networks with time delays

Author

Mohammad Ghousein, Emmanuel Moulay, Patrick Coirault, Laboratoire d'Informatique et d'Automatique pour les Systèmes (LIAS), Université de Poitiers-ENSMA, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), and Université de Poitiers

Subjects
0303 health sciences, Mechanical Engineering, General Chemical Engineering, Biomedical Engineering, Aerospace Engineering, 01 natural sciences, Industrial and Manufacturing Engineering, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 03 medical and health sciences, Control and Systems Engineering, 0103 physical sciences, Electrical and Electronic Engineering, 010306 general physics, ComputingMilieux_MISCELLANEOUS, 030304 developmental biology
Abstract

International audience

Published
2022

47. State feedback control and delay estimation for LTI system with unknown input-delay

Author

Emmanuel Moulay, Franck Plestan, Yang Deng, Vincent Léchappé, Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Commande (Commande), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Université de Poitiers, Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
Scheme (programming language), 0209 industrial biotechnology, Computer science, Lyapunov-Krasovskii functional, predictor-based controller, Feedback control, Control (management), 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science Applications, delay estimation, LTI system theory, 020901 industrial engineering & automation, Time-delay system, Exponential stability, Computer Science::Systems and Control, Control and Systems Engineering, Control theory, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, State (computer science), Constant (mathematics), computer, computer.programming_language
Abstract

International audience; The objective of this paper is to build feedback control solutions for LTI systems with unknown constant input-delay. The control scheme includes a time-delay estimation algorithm and a predictor-based controller. The Lyapunov-Krasovskii theorem provides the global exponential stability of the closed-loop system. Some examples illustrate the theoretical results and the performances of the proposed method.

Published
2020

48. Fixed-time sliding mode control with mismatched disturbances

Author

Emmanuel Moulay, Emmanuel Bernuau, Michael Defoort, Vincent Léchappé, Franck Plestan, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Paris-Saclay Food and Bioproduct Engineering (SayFood), AgroParisTech-Université Paris-Saclay-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201 (LAMIH), Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, and Nantes Université (Nantes Univ)

Subjects
fixed-time differentiator, 0209 industrial biotechnology, Sliding mode control, Computer science, 020208 electrical & electronic engineering, Mode (statistics), 02 engineering and technology, Differentiator, 020901 industrial engineering & automation, Control and Systems Engineering, Robustness (computer science), Fixed time, Control theory, fixed-time stability, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, mismatched disturbances
Abstract

International audience; The aim of this article is to develop new second-order fixed-time sliding mode controllers able to tackle mismatched disturbances. Contrary to what is done in the literature, the proposed sliding-mode control strategy does not use disturbance observers because the sliding surface possesses robustness properties. The results are applied to define a new fixed-time differentiator.

Published
2022

49. Properties of the sign gradient descent algorithms

Author

Franck Plestan, Emmanuel Moulay, Vincent Léchappé, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
Information Systems and Management, Computer science, metaheuristic, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Theoretical Computer Science, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, Initial value problem, Global optimization, Metaheuristic, Gradient descent, Rprop algorithm, 05 social sciences, 050301 education, Lyapunov sequence, Computer Science Applications, Maxima and minima, Control and Systems Engineering, discrete-time systems, 020201 artificial intelligence & image processing, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], optimization, 0503 education, Algorithm, Software, Sign (mathematics)
Abstract

The aim of this article is to study the properties of the sign gradient descent algorithms involving the sign of the gradient instead of the gradient itself and first introduced in the RPROP algorithm. This article provides two results of convergence for local optimization , a first one for nominal systems without uncertainty and a second one for systems with uncertainties. New sign gradient descent algorithms including the dichotomy algorithm DICHO are applied on several examples to show their effectiveness in terms of speed of convergence. As a novelty, the sign gradient descent algorithms can allow to converge in practice towards other minima than the closest minimum of the initial condition making these algorithms suitable for global optimization as a new metaheuristic method.

Published
2019

50. (µ, ν)−pseudo almost automorphic solutions of neutral type Clifford-valued high-order Hopfield neural networks with D operator

Author

Chaouki Aouiti, Farah Dridi, Qing Hui, Emmanuel Moulay, Faculté des Sciences de Bizerte [Université de Carthage], Université de Carthage - University of Carthage, University of Nebraska [Lincoln], University of Nebraska System, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), and Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Pure mathematics, Artificial neural network, Computer Networks and Communications, General Neuroscience, Operator (physics), Complex system, Computational intelligence, 02 engineering and technology, Fixed point, Type (model theory), [INFO.INFO-NE]Computer Science [cs]/Neural and Evolutionary Computing [cs.NE], 020901 industrial engineering & automation, Exponential stability, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Uniqueness, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Software, Mathematics
Abstract

International audience; The aim of this article is to study neutral type Clifford-valued highorder Hopfield neural networks with mixed delays and D operator. New criteria are established for the existence, uniqueness and global exponential stability of (µ, ν)−pseudo almost automorphic solutions of the considered model via Banach's fixed point principle and differential inequality techniques. An example is given to show the effectiveness of the main new criteria. Keywords Clifford algebra • High-order Hopfield neural network • (µ, ν)−pseudo almost automorphic function • D operator

Published
2021

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