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Locating fast-varying line disturbances with the frequency mismatch

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IFAC-PapersOnLine 2022年第13期55卷 270-275页

作者： Robin Delabays Laurent Pagnier Melvyn Tyloo Center for Control Dynamical Systems and Computation UCSB Santa Barbara CA 93106 USA Department of Mathematics University of Arizona Tucson AZ 85721 USA Theoretical Division Los Alamos National Laboratory Los Alamos NM 87545 USA

In an attempt to provide an efficient method for line disturbance identification in complex networks of diffusively coupled agents, we recently proposed to leverage the frequency mismatch . The frequency mismatch filters out the intricate combination of interactions induced by the network structure and quantifies to what extent the trajectory of each agent is affected by the disturbance. In this previous work, we provided some analytical evidence of its efficiency when the perturbation is assumed to be slow . In the present work, we claim that the frequency mismatch performs actually well for most disturbance regimes. This is shown through a series of simulations and is backed up by an analytical argument. Therefore, we argue that the frequency mismatch is an efficient and elegant tool for line disturbance location in complex networks of diffusively coupled agents.

关键词： Networks inference fault attack detection

Finite-Time Stability of ABC Type ℏ-Fractional Discrete Neural Networks: Gronwall Inequality and Stability Criterion

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Finite-Time Stability of ABC Type ℏ-Fractional Discrete Neu...

International Conference on Fractional Differentiation and Its Applications (ICFDA)

作者： Amel Hioual Adel Ouannas Shaher Momani Taki-Eddine Oussaeif Laboratory of Dynamical Systems and Control University of Oum EL-Bouaghi Algeria Department of Mathematics and Computer Science University of Oum EL-Bouaghi Algeria Nonlinear Dynamics Research Center (NDRC) Ajman University Ajman UAE Department of Mathematics The University of Jordan Amman Jordan

The dynamics of fractional-order difference neural networks are currently a major research area, with several noteworthy discoveries. The dynamics of discrete-time neural networks with $\hbar$-fractional nonlocal and nonsingular kernels, on the other hand, have not been thoroughly researched, and this paper is one of the first to address this subject. The main focus of this research is the finite-time stability of discrete-time neural networks based on the nabla ABC fractional difference operator. First, the Atangana-Baleanu $\hbar$-fractional difference sum operator is used to investigate a generalized $\hbar$-Gronwall inequality. This inequality also yields the uniqueness theorem and the finite-time stability criterion of nonlinear $\hbar$-fractional neural networks. Finally, several examples are offered to show the effectiveness of our theoretical conclusion.

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Fractional discrete neural networks with variable order: solvability, finite time stability and synchronization

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The European Physical Journal Special Topics 2024年 1-14页

作者： Hioual, Amel Alomari, Saleh Al-Tarawneh, Hassan Ouannas, Adel Grassi, Giuseppe Laboratory of Dynamical Systems and Control University of Oum El-Bouaghi Oum El Bouaghi Algeria Faculty of Science and Information Technology Software Engineering Jadara University Irbid Jordan Department of Data Sciences and Artificial Intelligence Al-Ahliyya Amman University Amman Jordan Department of Mathematics and Computer Science University of Oum EL-Bouaghi Oum El Bouaghi Algeria Dipartimento Ingegneria Innovazione Universita del Salento Lecce Italy

Research in the field of dynamic behaviors in neural networks with variable-order differences is currently a thriving area, marked by various significant discoveries. However, when it comes to discrete-time neural networks featuring fractional variable-order nonlocal and nonsingular kernels, there has been limited exploration. This paper stands as one of the initial contributions to this subject, focusing primarily on the topics of stability and synchronization in finite-time within discrete neural networks. The research employs the nabla ABC variable-order difference operator, with a primary approach involving the investigation of a novel Gronwall inequality using the Atangana-Baleanu difference variable-order sum operator. This analysis leads to the development of a uniqueness theorem and a criterion for the stability in finite-time of variable-order discrete neural networks. Furthermore, the requirements stemming from this type of stability and the novel Gronwall inequality serve as the foundation for establishing the conditions necessary for achieving finite-time synchronization in these networks, employing a specific control using state feedback method. Finally, the study utilizes numerical solutions to validate the obtained results.

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Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learning

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arXiv 2024年

作者： He, Fan He, Mingzhen Shi, Lei Huang, Xiaolin Suykens, Johan A.K. STADIUS Center for Dynamical Systems Signal Processing and Data Analytics KU Leuven Leuven Belgium MOE Key Laboratory of System Control and Information Processing Institute of Image Processing and Pattern Recognition Shanghai Jiao Tong University Shanghai China Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai200433 China Shanghai Artificial Intelligence Laboratory Shanghai200232 China MOE Key Laboratory of System Control and Information Processing Institute of Image Processing and Pattern Recognition Institute of Medical Robotics Shanghai Jiao Tong University Shanghai200240 China

Ridgeless regression has garnered attention among researchers, particularly in light of the "Benign Overfitting" phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression does not always perform well due to the lack of flexibility. This paper enhances kernel ridgeless regression with Locally-Adaptive-Bandwidths (LAB) RBF kernels, incorporating kernel learning techniques to improve performance in both experiments and theory. For the first time, we demonstrate that functions learned from LAB RBF kernels belong to an integral space of Reproducible Kernel Hilbert Spaces (RKHSs). Despite the absence of explicit regularization in the proposed model, its optimization is equivalent to solving an 0-regularized problem in the integral space of RKHSs, elucidating the origin of its generalization ability. Taking an approximation analysis viewpoint, we introduce an lq-norm analysis technique (with 0 © 2024, CC BY.

关键词： Vector spaces

Convergence, Consensus and Dissensus in the Weighted-Median Opinion Dynamics

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arXiv 2022年

作者： Mei, Wenjun Hendrickx, Julien M. Chen, Ge Bullo, Francesco Dörfler, Florian The Department of Mechanics and Engineering Science Peking University China The Institute of Information and Communication Technologies Electronics and Applied Mathematics UCLouvain Belgium The Academy of Mathematics and Systems Science Chinese Academy of Sciences China The Center of Control Dynamical-Systems and Computation University of California Santa Barbara United States Automatic Control Laboratory ETH Zurich Switzerland

Mechanistic and tractable mathematical models play a key role in understanding how social influence shapes public opinions. Recently, a weighted-median mechanism has been proposed as a new micro-foundation of opinion dynamics and validated via experimental data. Numerical studies also indicate that this new mechanism recreates some non-trivial real-world features of opinion evolution. In this paper, we conduct a thorough theoretical analysis of the weighted-median opinion dynamics. We fully characterize the set of all equilibria, and we establish the almost-sure finite-time convergence for any initial condition. Moreover, we prove a necessary and sufficient graph-theoretic condition for the almost-sure convergence to consensus, as well as a sufficient graph-theoretic condition for almost-sure persistent dissensus. It turns out that the weighted-median opinion dynamics, despite its simplicity in form, exhibit rich dynamical behavior that depends on some delicate network structures. To complement our sufficient conditions for almost-sure dissensus, we further prove that, given the influence network, determining whether the system almost surely achieves persistent dissensus is NP-hard, which reflects the complexity the network topology contributes to opinion *** Codes 93E03, 93A30, 91D30 Copyright © 2022, The Authors. All rights reserved.

关键词： Network topology

Topological entropy of switched nonlinear and interconnected systems

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arXiv 2023年

作者： Yang, Guosong Liberzon, Daniel Hespanha, João P. The Department of Electrical and Computer Engineering Rutgers University PiscatawayNJ08854 United States The Coordinated Science Laboratory University of Illinois Urbana-Champaign UrbanaIL61801 United States The Center for Control Dynamical Systems and Computation University of California Santa Barbara Santa BarbaraCA93106 United States

A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their active rates. A general lower bound is constructed as well, using a similar weighted average of lower limits of the traces of these Jacobian matrices. In a case of interconnected structure, the general upper bound is readily applied to derive upper bounds for entropy that depend only on "network-level" information. In a case of block-diagonal structure, less conservative upper and lower bounds for entropy are constructed. In each case, upper bounds for entropy that require less information about the switching signal are also derived. The upper bounds for entropy and their relations are illustrated by numerical examples of a switched Lotka–Volterra ecosystem *** Codes 37B40, 93C30 (Primary) 93C57 (Secondary) © 2023, CC BY-NC-ND.

关键词： Jacobian matrices

Biologically plausible robust control with Neural Network weight reset for unmanned aircraft systems under impulsive disturbances

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Biologically plausible robust control with Neural Network we...

American control Conference (ACC)

作者： Ignacio Rubio Scola Luis Rodolfo Garcia Carrillo Andrew T. Sornborger João P. Hespanha Department of Industrial Products Engineering INTI CONICET and UNR Rosario Argentina Klipsch School of Electrical and Computer Engineering New Mexico State University Las Cruces NM USA Los Alamos National Laboratory Los Alamos NM USA Center for Control Dynamical Systems and Computation University of California Santa Barbara USA

Self-learning control techniques mimicking the functionality of the limbic system in the mammalian brain have shown advantages in terms of superior learning ability and low computational cost. However, accompanying stability analyses and mathematical proofs rely on unrealistic assumptions which limit not only the performance, but also the implementation of such controllers in real-world scenarios. In this work the limbic system inspired control (LISIC) framework is revisited, introducing three contributions that facilitate the implementation of this type of controller in real-time. First, an extension enabling the implementation of LISIC to the domain of SISO affine systems is proposed. Second, a strategy for resetting the controller’s Neural Network (NN) weights is developed, in such a way that now it is possible to deal with piece-wise smooth references and impulsive perturbations. And third, for the case when a nominal model of the system is available, a technique is proposed to compute a set of optimal NN reset weight values by solving a convex constrained optimization problem. Numerical simulations addressing the stabilization of an unmanned aircraft system via the robust LISIC demonstrate the advantages obtained when adopting the extension to SISO systems and the two NN weight reset strategies.

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Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control

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Chinese Physics B 2020年第5期29卷 174-181页

作者： Adel Ouannas Amina Aicha Khennaoui Shaher Momani Viet-Thanh Pham Reyad El-Khazali Laboratory of Mathematics Informatics and Systems(LAMIS)University of Laarbi TebessiTebessa12002Algeria College of Humanities and Sciences Ajman UniversityAjmanUAE Laboratory of Dynamical Systems and Control University of Larbi Ben M’hidiOum El BouaghiAlgeria Department of Mathematics Faculty of ScienceUniversity of JordanAmman 11942Jordan Nonlinear Systems and Applications Faculty of Electrical and Electronics EngineeringTon Duc Thang UniversityHo Chi Minh CityVietnam ECCE Department Khalifa UniversityAbu-Dhabi 127788United Arab Emirates

This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference *** is the first study to explore a three-dimensional fractional-order discrete chaotic system without *** phase portrait,bifurcation diagrams,and largest Lyapunov exponents,it is shown that the proposed fractional-order discrete system exhibits a range of different dynamical ***,different tests are used to confirm the existence of chaos,such as 0-1 test and C0 *** addition,the quantification of the level of chaos in the new fractional-order discrete system is measured by the approximate entropy ***,based on the fractional linearization method,a one-dimensional controller to stabilize the new system is *** results are presented to validate the findings of the paper.

关键词： discrete chaos discrete fractional calculus hidden attractor

Locating fast-varying line disturbances with the frequency mismatch

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arXiv 2022年

作者： Delabays, Robin Pagnier, Laurent Tyloo, Melvyn Center for Control Dynamical Systems and Computation UCSB Santa BarbaraCA93106 United States Department of Mathematics University of Arizona TucsonAZ85721 United States Theoretical Division Los Alamos National Laboratory Los AlamosNM87545 United States

In an attempt to provide an efficient method for line disturbance identification in complex networks of diffusively coupled agents, we recently proposed to leverage the frequency mismatch. The frequency mismatch filters out the intricate combination of interactions induced by the network structure and quantifies to what extent the trajectory of each agent is affected by the disturbance. In this previous work, we provided some analytical evidence of its efficiency when the perturbation is assumed to be slow. In the present work, we claim that the frequency mismatch performs actually well for most disturbance regimes. This is shown through a series of simulations and is backed up by an analytical argument. Therefore, we argue that the frequency mismatch is an efficient and elegant tool for line disturbance location in complex networks of diffusively coupled agents. © 2022, CC BY-NC-ND.

关键词： Complex networks