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Finite-time Bipartite Synchronization of Homogeneous and Heterogeneous Multiple Agents with Input Saturation: A TVRE-based Gain Approach

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IEEE Transactions on Automatic Control 2025年

作者： Zhou, Yuan Liu, Yongfang Zhao, Yu Li, Zhongkui Hong Kong Polytechnic University Department of Applied Mathematics Hung Hom Hong Kong Northwestern Polytechnical University School of Automation Xi'an China Peking University State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering Science College of Engineering Beijing100871 China

Pursuing faster convergence rates and smaller input magnitudes seem to be two conflicting goals in studying multi-agent systems. To give a trade-off between the two, this paper focuses on the bipartite synchronization problems over signed topologies and aims to achieve finite-time control for general linear agents subject to input saturation constraints. Firstly, this paper considers homogeneous agents and presents a class of bipartite synchronization protocols with saturation constraint, which exploits the solution of the time-varying Riccati equation (TVRE) to design the control gain. Then, a time-varying parameter scheduler is tactically designed for TVRE and achieves finite-time bipartite synchronization. Note that the design uses the solution computed online and brings a bit of conservatism in determining the settling time. So, for heterogeneous agents, this paper constructs a modified parameter scheduler computed off-line to reduce the conservatism. A class of finite-time bipartite synchronization generators and generator-based finite-time protocols are proposed. It shows that, in both designs, the control input subjects to the bound saturation during convergence even if the gain escapes to infinity towards the settling time. Moreover, the trade-off among the finite convergence time, the saturation bound of the input, and the initial domain are analyzed explicitly in theory. Finally, two simulations verify the validity of the theoretical results. © 1963-2012 IEEE.

关键词： Synchronization

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Amplification of Waves with Broad Frequency Spectrum in FEL with Longitudinal Electrostatic Undulator

Amplification of Waves with Broad Frequency Spectrum in FEL ...

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2020 IEEE Ukrainian Microwave Week, UkrMW 2020

作者： Lysenko, Alexander Volk, Iurii Brusnyk, Alla Korovai, Mykhailo Koval, Vitaliy Sumy State University Department of Applied Mathematics and Complex Systems Modeling Sumy Ukraine Sumy State University Department of Electronics General and Applied Physics Sumy Ukraine

ISBN: (纸本)9781728173139

Within the cubic nonlinear approximation framework we performed the analysis of space charge waves (SCWs) with broad frequency spectrum amplification in superheterodyne free electron laser (FEL) with longitudinal electrostatic undulator. We found out that the system under study allows realization of plural resonances of two types. We showed that in such FEL the SCW growth rates do not depend on the frequencies of the amplified waves. The lengths at which the SCW with broad frequency spectrum amplification occurs without distorting its shape are determined. © 2020 IEEE.

关键词： Electrostatics

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GLOBAL-IN-TIME ENERGY STABILITY ANALYSIS FOR THE EXPONENTIAL TIME DIFFERENCING RUNGE–KUTTA SCHEME FOR THE PHASE FIELD CRYSTAL EQUATION

arXiv

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arXiv 2024年

作者： Li, Xiao Qiao, Zhonghua Wang, Cheng Zheng, Nan Key Laboratory of Mathematics and Complex Systems Ministry of Education School of Mathematical Sciences Beijing Normal University Beijing100875 China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong Mathematics Department The University of Massachusetts North DartmouthMA02747 United States

The global-in-time energy estimate is derived for the second-order accurate exponential time differencing Runge–Kutta (ETDRK2) numerical scheme to the phase field crystal (PFC) equation, a sixth-order parabolic equation modeling crystal evolution. To recover the value of stabilization constant, some local-in-time convergence analysis has been reported, and the energy stability becomes available over a fixed final time. In this work, we develop a global-in-time energy estimate for the ETDRK2 numerical scheme to the PFC equation by showing the energy dissipation property for any final time. An a priori assumption at the previous time step, combined with a single-step H2 estimate of the numerical solution, is the key point in the analysis. Such an H2 estimate recovers the maximum norm bound of the numerical solution at the next time step, and then the value of the stabilization parameter can be theoretically justified. This justification ensures the energy dissipation at the next time step, so that the mathematical induction can be effectively applied, by then the global-in-time energy estimate is accomplished. This paper represents the first effort to theoretically establish a global-in-time energy stability analysis for a second-order stabilized numerical scheme in terms of the original free energy functional. The presented methodology is expected to be available for many other Runge–Kutta numerical schemes to the gradient flow equations. © 2024, CC BY.

关键词： Energy dissipation

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Why Fuzzy Control Is Often More Robust (and Smoother): A Theoretical Explanation

Why Fuzzy Control Is Often More Robust (and Smoother): A The...

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2023 IEEE Symposium Series on Computational Intelligence, SSCI 2023

作者： Csiszar, Orsolya Csiszar, Gabor Kosheleva, Olga Ceberio, Martine Kreinovich, Vladik Research Center for Complex Systems Aalen University Germany Óbuda University Institute of Applied Mathematics John von Neumann Faculty of Informatics Hungary Óbuda University Biomatics and Applied Ai Institute John von Neumann Faculty of Informatics Hungary University of Texas at El Paso Department of Teacher Education El PasoTX United States University of Texas at El Paso Department of Computer Science El PasoTX United States

ISBN: (纸本)9781665430654

In many practical situations, practitioners use easier-to-compute fuzzy control to approximate the more-difficult-to-compute optimal control. As expected, for many characteristics, this approximate control is slightly worse than the optimal control it approximates. However, with respect to robustness or smoothness, the approximating fuzzy control is often better than the original one. In this paper, we provide a theoretical explanation for this somewhat mysterious empirical phenomenon. © 2023 IEEE.

关键词： fuzzy control robust control smooth control

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Microstructure and High-hardness Effect in TiSiN/NbN Nanomultilayers: Experimental Research 11

Microstructure and High-hardness Effect in TiSiN/NbN Nanomul...

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11th IEEE International Conference "Nanomaterials: Applications and Properties", NAP 2021

作者： Beresnev, V.M. Lytovchenko, S.V. Maksakova, O.V. Pogrebnjak, A.D. Horokh, D.V. Shvets, U.S. Department of Materials for Reactor Building and Physical Technologies V.N. Karazin Kharkiv National University Kharkiv Ukraine Department of Nanoelectronics and Surface Modification Sumy State University Sumy Ukraine Department of Applied Mathematics and Complex Systems Modeling Sumy State University Sumy Ukraine

ISBN: (纸本)9781665439077

Nanoscale multilayer TiSiN/NbN coatings with a modulation period ranging from 75 to 50 nm were deposited onto steel using the cathodic arc physical vapor deposition technique. The microstructure of multilayer TiSiN/NbN coatings was nanocomposite consisting of nanocrystallite phases fcc-TiN and hcp- NbN-δ'. With the increase of the bias potential from -110 to -200 V, the silicon content in multilayers decreased two times from 1.9 to 0.8 at. %, whereas nitrogen content was nearly constant (>30 at. %). A dense structure consisting of flat and well-defined hard TiSiN and NbN nanolayers led to high mechanical indicators. At modulation period of 50 nm, the hardness reached a maximum of 40 GPa and Young’s modulus of 560 GPa. The values of H/E and H3/E2 ratios were respectively in the ranges of (0.066-0.071) and (0.14-0.2). ©2021 IEEE

关键词： Hardness

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Hypocenter Relocation, Determination of Velocity Model and Correction Station in Gede Volcano for December 2017 Data 8

Hypocenter Relocation, Determination of Velocity Model and C...

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8th Asian Physics Symposium, APS 2019

作者： Reny Srigutomo, W. Faizi, H.N. Modeling and Inversion Laboratory Physics of Earth and Complex Systems Department of Physics Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jl. Ganesa 10 Bandung40123 Indonesia

The distribution of the volcanoes in indonesia gives positive impacts in the form of fertile land where many residents live to grow crops. Besides having positive impacts, there are also negative impacts in the form of natural disasters. Improvement in mitigation of natural disasters is needed to avoid any form of harm and undesired losses. Information on the accuracy of earthquake parameters is an important part of natural disaster mitigation efforts. Hypocenter relocation of earthquakes is a step to improve the accuracy of earthquake parameter information. The relocation of hypocenters earthquake is performed using the Coupled Velocity-Hypocenter method. The research area is Gede volcano which is included as type A active volcanoes. The data were processed using GAD and VELEST 3.3 software resulted in epicenters that were spread around Gede and Pangrango volcanoes. The hypocentre were distributed between -2.5 - 5.2 km depths based on GAD calculated. After relocation using VELEST 3.3, they were distributed between 1.0 - 10.5 km depth. The calculated. The calculated magnitudes of volcanic earthquakes occurred in December 2017 vary between 0.6 to 2.7. the difference between the initial and final velocity models is small. After station correction step, the velocity profiles beneath the most of station is indicated as sedimentary layers, and beneath of the peak station, it is indicated as instrusive rocks. © Published under licence by IOP Publishing Ltd.

关键词： Velocity

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Path Percolation in Quantum Communication Networks

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Physical Review Letters 2025年第3期134卷 030803-030803页

作者： Xiangyi Meng Bingjie Hao Balázs Ráth István A. Kovács Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute Troy New York 12180 USA Department of Physics and Astronomy Northwestern University Evanston Illinois 60208 USA Department of Stochastics Institute of Mathematics Budapest University of Technology and Economics H-1111 Budapest Hungary HUN-REN-BME Stochastics Research Group H-1111 Budapest Hungary Alfréd Rényi Institute of Mathematics H-1053 Budapest Hungary Northwestern Institute on Complex Systems Northwestern University Evanston Illinois 60208 USA Department of Engineering Sciences and Applied Mathematics Northwestern University Evanston Illinois 60208 USA

In a quantum communication network, links represent entanglement between qubits located at different nodes. Even if two nodes are not directly linked by shared entanglement, they can still communicate via routing protocols. However, in contrast to classical communication, each quantum communication event removes all participating links along the routed path, disrupting the quantum communication network. Here, we propose a simple model, where randomly selected pairs of nodes communicate through the shortest paths. Each time such a path is used, all participating links are eliminated, leading to a correlated percolation process that we call “path percolation.” We study path percolation both numerically and analytically and present the phase diagram of the steady states as a function of the rate at which new links are being added to the network. As a key result, the steady state is found to be independent of the initial network topologies when new links are added randomly between disconnected components. We close by discussing extensions of path percolation and link replenishment, along with their potential applications.

关键词： Quantum entanglement

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Using LDLT factorizations in Newton's method for solving general large-scale algebraic Riccati equations

arXiv

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arXiv 2024年

作者： Saak, Jens Werner, Steffen W.R. Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstraße 1 Magdeburg39106 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

Continuous-time algebraic Riccati equations can be found in many disciplines in different forms. In the case of small-scale dense coefficient matrices, stabilizing solutions can be computed to all possible formulations of the Riccati equation. This is not the case when it comes to large-scale sparse coefficient matrices. In this paper, we provide a reformulation of the Newton-Kleinman iteration scheme for continuous-time algebraic Riccati equations using indefinite symmetric low-rank factorizations. This allows the application of the method to the case of general large-scale sparse coefficient matrices. We provide convergence results for several prominent realizations of the equation and show in numerical examples the effectiveness of the *** Codes 15A24, 49M15, 65F45, 65H10, 93A15 Copyright © 2024, The Authors. All rights reserved.

关键词： Continuous time systems

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Ancient Solutions to the Parabolic Monge–Ampère Equations with New Asymptotic Behavior at Infinity

SSRN

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SSRN 2024年

作者： Bao, Jiguang Liu, Zixiao Zhou, Ziwei School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing100875 China Institute of Applied Mathematics Department of Mathematics School of Mathematics Statistics and Mechanics Beijing University of Technology Beijing100124 China School of Statistics University of International Business and Economics Beijing100029 China

Demonstrating new asymptotic behavior u − u1 = o(1) at infinity, we employ the Perron method to establish the existence of ancient solutions to exterior Dirichlet problems associated with the parabolic Monge–Amp`ere equation −ut · det D2u = f, where f is asymptotic to 1 at infinity. The function u1 has unbounded and not strictly negative partial derivative with respect to time variable, and it represents a new family of smooth, parabolically convex, ancient entire solutions to the equation with f ≡ 1. The family of solutions was recently discovered in [An–Bao–Liu, Nonlinear Anal., 2024], and their asymptotic behavior differs significantly from the scenario where ut is bounded and strictly negative. In contrast to existing methodologies in the study of exterior Dirichlet problems, functions relying only on the value of u1 have been introduced to replace generalized symmetric functions. © 2024, The Authors. All rights reserved.

关键词： Choquet integral

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H2 optimal model reduction of linear systems with multiple quadratic outputs

arXiv

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arXiv 2024年

作者： Reiter, Sean Duff, Igor Pontes Gosea, Ion Victor Gugercin, Serkan Department of Mathematics Virginia Tech BlacksburgVA24061 United States Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

In this work, we consider the H2 optimal model reduction of dynamical systems that are linear in the state equation and up to quadratic nonlinearity in the output equation. As our primary theoretical contributions, we derive gradients of the squared H2 system error with respect to the reduced model quantities and, from the stationary points of these gradients, introduce Gramian-based first-order necessary conditions for the H2 optimal approximation of a linear quadratic output (LQO) system. The resulting H2 optimality framework neatly generalizes the analogous Gramian-based optimality framework for purely linear systems. Computationally, we show how to enforce the necessary optimality conditions using Petrov-Galerkin projection;the corresponding projection matrices are obtained from a pair of Sylvester equations. Based on this result, we propose an iteratively corrected algorithm for the H2 model reduction of LQO systems, which we refer to as LQO-TSIA (linear quadratic output two-sided iteration algorithm). Numerical examples are included to illustrate the effectiveness of the proposed computational method against other existing *** Codes 15A24, 46N10, 49K15, 93A15, 93C10, 93C80 Copyright © 2024, The Authors. All rights reserved.

关键词： Linear systems

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