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Convergence Properties of the Heterogeneous Deffuant-Weisbuch Model

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arXiv 2019年

作者： Chen, Ge Su, Wei Mei, Wenjun Bullo, Francesco National Center for Mathematics and Interdisciplinary Sciences Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing100083 China Automatic Control Laboratory ETH Zurich8092 Switzerland Department of Mechanical Engineering The Center of Control Dynamical-Systems and Computation University of California Santa BarbaraCA93106-5070 United States

The Deffuant-Weisbuch (DW) model is a bounded-confidence opinion dynamics model that has attracted much recent interest. Despite its simplicity and appeal, the DW model has proved technically hard to analyze and its most basic convergence properties, easy to observe numerically, are only conjectures. This paper solves the convergence problem for the heterogeneous DW model with the weighting factor not less than 1/2. We establish that, for any positive confidence bounds and initial values, the opinion of each agent will converge to a limit value almost surely, and the convergence rate is exponential in mean square. Moreover, we show that the limiting opinions of any two agents either are the same or have a distance larger than the confidence bounds of the two agents. Finally, we provide some sufficient conditions for the heterogeneous DW model to reach *** Codes 93E03, 93A30, 91D30 Copyright © 2019, The Authors. All rights reserved.

关键词： Economic and social effects

On Topological Entropy of Switched Linear systems with Diagonal, Triangular, and General Matrices 57

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On Topological Entropy of Switched Linear Systems with Diago...

57th IEEE Conference on Decision and control, CDC 2018

作者： Yang, Guosong James Schmidt, A. Liberzon, Daniel University of California Center for Control Dynamical Systems and Computation Santa BarbaraCA93106 United States University of Illinois at Urbana-Champaign Coordinated Science Laboratory UrbanaIL61801 United States

ISBN: (纸本)9781538613955

This paper introduces a notion of topological entropy for switched systems, formulated using the minimal number of initial states needed to approximate all initial states within a finite precision. We show that it can be equivalently defined using the maximal number of initial states separable within a finite precision, and introduce switching-related quantities such as the active time of each mode, which prove to be useful in calculating the topological entropy of switched linear systems. For general switched linear systems, we show that the topological entropy is independent of the set of initial states, and establish upper and lower bounds using the active-time-weighted averages of the norms and traces of system matrices in individual modes, respectively. For switched linear systems with scalar-valued state or simultaneously diagonalizable matrices, we derive formulae for the topological entropy using active-time-weighted averages of eigenvalues, which can be extended to the case with simultaneously triangularizable matrices to obtain an upper bound. In these three cases with special matrix structure, we also provide more general but more conservative upper bounds for the topological entropy. © 2018 IEEE.

关键词： Matrix algebra

A brief survey on singularities of geodesic flows in smooth signature changing metrics on 2-surfaces 2nd

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A brief survey on singularities of geodesic flows in smooth ...

2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015

作者： Pavlova, N.G. Remizov, A.O. Department of Nonlinear Analysis and Optimization RUDN University Moscow Russia V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences Moscow Russia Laboratory of Dynamical Systems National Research University Higher School of Economics Moscow Russia

ISBN: (纸本)9783319736389

We present a survey on generic singularities of geodesic flows in smooth signature changing metrics (often called pseudo-Riemannian) in dimension 2. Generically, a pseudo-Riemannian metric on a 2-manifold S changes its signature (degenerates) along a curve S0, which locally separates S into a Riemannian (R) and a Lorentzian (L) domain. The geodesic flow does not have singularities over R and L, and for any point q∈ R∪ L and every tangential direction p∈ there exists a unique geodesic passing through the point q with the direction p. On the contrary, geodesics cannot pass through a point q∈ S0 in arbitrary tangential directions, but only in some admissible directions;the number of admissible directions is 1 or 2 or 3. We study this phenomenon and the local properties of geodesics near q∈ S0. © Springer International Publishing AG, part of Springer Nature 2018.

关键词： Surveys

A Robust State Estimator for Multi-Agent systems Under Impulsive Noise and Missing Measurements

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A Robust State Estimator for Multi-Agent Systems Under Impul...

IEEE Annual Conference on Decision and control

作者： Junfei Xie Luis Rodolfo Garcia Carrillo Lei Jin Joao P. Hespanha Department of Electrical and Computer Engineering San Diego State University San Diego CA Unmanned Systems Laboratory (TAMUCC-USL) Texas A&M University - Corpus Christi Corpus Christi TX Department of Department of Mathematics & Statistics Texas A&M University-Corpus Christi Center for Control Dynamical Systems and Computation University of California Santa Barbara CA USA

ISBN: (数字)9781728113982

ISBN: (纸本)9781728113999

We address the problem of estimating the state of a Multi-Agent System (MAS) with dynamics subjected to impulsive disturbances, based on measurements that are corrupted with impulsive noise and are sometimes missing. To facilitate the online implementation of the proposed state estimator for MAS, a graph formulation is proposed first. Then, making use of the Huber Loss, the estimator adopts a general cost function that addresses missing measurements and is robust to impulsive noise and disturbances. The solution is validated under a synthetic scenario, where a team of UAVs equipped with onboard video cameras, inertial sensors, transceivers, and GPS, cooperatively geolocate and track a ground moving target agent. Comparison results with respect to three different state-of-the-art estimators are provided to show the superior performance and benefits of the proposed robust estimator.

关键词： Noise measurement Sensors Global Positioning System Robustness Loss measurement Time measurement Current measurement

Novel multi-agent models for chemical self-assembly

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arXiv 2018年

作者： Ning, Zheng Chen, Ge Bullo, Francesco National Center for Mathematics and Interdisciplinary Sciences Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Department of Mechanical Engineering Center of Control Dynamical-Systems and Computation University of California at Santa Barbara CA93106-5070 United States

The chemical self-assembly has been considered as one of most important scientific problems in the 21th Century;however, since the process of self-assembly is very complex, there is few mathematic theory for it currently. This paper provides a novel multi-agent model for chemical self-assembly, where the interaction between agents adopts the classic Lennard-Jones potential. Under this model, we propose an optimal problem by taking the temperature as the control input, and choosing the internal energy as the optimal object. A numerical solution for our optimal problem is also developed. Simulations show that our control scheme can improve the product of self-assembly. Further more, we give a strict analysis for the self-assembly model without noise, which corresponds to an attraction-repulsion multi-agent system, and prove it converges to a stable configuration eventually. Copyright © 2018, The Authors. All rights reserved.

关键词： Multi agent systems

Design, build and integration of a low-cost self-erecting inverted pendulum mechanism

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Design, build and integration of a low-cost self-erecting in...

AIAA Modeling and Simulation Technologies Conference, 2017

作者： Graham, Brian Turkoglu, Kamran Control Science and Dynamical Systems Laboratory San Jose State University San JoseCA95192 United States San Jose State University San JoseCA95192 United States

ISBN: (纸本)9781624104510

This paper details the designing, building and the controller design/implementation of a self-erecting inverted pendulum setup on a cart as a teaching and research platform. The setup was built with off-the-shelf, low cost, widely available equipments to balance a pendulum in an unstable position as well as control the cart position with only one input. A preliminary model was first implemented using two PID controllers in Simulink. The real physical setup was then modeled using frequency based system identification techniques as well as using the equations of motion to develop accurate transfer functions. The setup is programmed using Arduino, and the system can swing up as well as balance the pendulum while maintaining cart position control for a given bounded disturbance, showing robustness of the developed set-up as well. © 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

关键词： Inverted pendulum

A Robust Ensemble Algorithm for Ischemic Stroke Lesion Segmentation: Generalizability and Clinical Utility Beyond the ISLES Challenge

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arXiv 2024年

作者： de la Rosa, Ezequiel Reyes, Mauricio Liew, Sook-Lei Hutton, Alexandre Wiest, Roland Kaesmacher, Johannes Hanning, Uta Hakim, Arsany Zubal, Richard Valenzuela, Waldo Robben, David Sima, Diana M. Anania, Vincenzo Brys, Arne Meakin, James A. Mickan, Anne Broocks, Gabriel Heitkamp, Christian Gao, Shengbo Liang, Kongming Zhang, Ziji Siddiquee, Md Mahfuzur Rahman Myronenko, Andriy Ashtari, Pooya Van Huffel, Sabine Jeong, Hyun-Su Yoon, Chi-Ho Kim, Chulhong Huo, Jiayu Ourselin, Sebastien Sparks, Rachel Clèrigues, Albert Oliver, Arnau Lladó, Xavier Chalcroft, Liam Pappas, Ioannis Bertels, Jeroen Heylen, Ewout Moreau, Juliette Hatami, Nima Frindel, Carole Qayyum, Abdul Mazher, Moona Puig, Domenec Lin, Shao-Chieh Juan, Chun-Jung Hu, Tianxi Boone, Lyndon Goubran, Maged Liu, Yi-Jui Wegener, Susanne Kofler, Florian Ezhov, Ivan Shit, Suprosanna Hernandez Petzsche, Moritz R. Menze, Bjoern Kirschke, Jan S. Wiestler, Benedikt Department of Quantitative Biomedicine University of Zurich Zurich Switzerland Department of Informatics Technical University Munich Germany Icometrix Leuven Belgium ARTORG Center for Biomedical Research University of Bern Bern Switzerland Department of Radiation Oncology University Hospital Bern University of Bern Switzerland University of Bern Bern Switzerland Chan Division of Occupational Science and Occupational Therapy University of Southern California Los AngelesCA United States Stevens Neuroimaging and Informatics Institute Department of Neurology Keck School of Medicine University of Southern California United States University Institute of Diagnostic and Interventional Neuroradiology Inselspital Bern Switzerland University Institute of Diagnostic and Interventional Neuroradiology University Hospital Bern Inselspital University of Bern Bern Switzerland Department of Diagnostic and Interventional neuroradiology University Medical Center Hamburg-Eppendorf Hamburg Germany Department of Medical Imaging Radboud University Medical Center Institute for Health Sciences Nijmegen Netherlands Deepwise AI Lab Beijing China Beijing University of Posts and Telecommunications Bejing China School of Computing and Augmented Intelligence Arizona State University TempeAZ United States NVIDIA Santa ClaraCA United States STADIUS Center for Dynamical Systems Signal Processing and Data Analytics KU Leuven Leuven Belgium Pohang Korea Republic of School of Biomedical Engineering & Imaging Sciences King’s College London United Kingdom Institute of Computer Vision and Robotics University of Girona Spain Wellcome Centre for Human Neuroimaging University College London London United Kingdom Laboratory of Neuro Imaging Stevens Institute for Neuroimaging and Informatics Keck School of Medicine University of Southern California Los Angeles United States KU Leuven Leuven Belgium CREATIS Université Lyon1 CNRS UMR5220 INSERM U1206 INSA-Lyon Villeurbanne696

Diffusion-weighted MRI (DWI) is essential for stroke diagnosis, treatment decisions, and prognosis. However, image and disease variability hinder the development of generalizable AI algorithms with clinical value. We address this gap by presenting a novel ensemble algorithm derived from the 2022 Ischemic Stroke Lesion Segmentation (ISLES) challenge. ISLES’22 provided 400 patient scans with ischemic stroke from various medical centers, facilitating the development of a wide range of cutting-edge segmentation algorithms by the research community. By assessing them against a hidden test set, we identified strengths, weaknesses, and potential biases. Through collaboration with leading teams, we combined top-performing algorithms into an ensemble model that overcomes the limitations of individual solutions. Our ensemble model combines the individual algorithms’ strengths and achieved superior ischemic lesion detection and segmentation accuracy (median Dice score: 0.82, median lesion-wise F1 score: 0.86) on our internal test set compared to individual algorithms. This accuracy generalized well across diverse image and disease variables. Furthermore, the model excelled in extracting clinical biomarkers like lesion types and affected vascular territories. Notably, in a Turing-like test, neuroradiologists consistently preferred the algorithm’s segmentations over manual expert efforts, highlighting increased comprehensiveness and precision. Validation using a real-world external dataset (N=1686) confirmed the model’s generalizability (median Dice score: 0.82, median lesion-wise F1 score: 0.86). The algorithm’s outputs also demonstrated strong correlations with clinical scores (admission NIHSS and 90-day mRS) on par with or exceeding expert-derived results, underlining its clinical relevance. This study offers two key findings. First, we present an ensemble algorithm that detects and segments ischemic stroke lesions on DWI across diverse scenarios on par with expert (neuro)rad

关键词： Diagnosis

A Numerical Implementation of an Extended Luenberger Observer for a Class of Semilinear Hyperbolic PIDEs

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IFAC-PapersOnLine 2016年第8期49卷 216-221页

作者： Deutschmann, Andreas Jadachowski, Lukas Kugi, Andreas Automation and Control Institute Complex Dynamical Systems Group Vienna University of Technology Vienna Austria Christian Doppler Laboratory for Model-Based Process Control in the Steel Industry Vienna University of Technology Vienna Austria

In this paper, an extended Luenberger observer for a class of semilinear hyperbolic PIDEs is proposed to solve the problem of state estimation. The nonlinear observer error dynamics is linearized and then stabilized locally by applying the backstepping method for time-varying linear hyperbolic PIDEs presented recently. Since the resulting kernel equation is computationally quite expensive, a numerical algorithm is proposed to obtain the solution in an efficient way. Finally, this algorithm is applied to an example with multiple equilibrium points, and the influence of the design parameters on the stability is investigated in more detail. © 2016

关键词： Backstepping

Linear stochastic approximation algorithms and group consensus over random signed networks: A technical report with all proofs

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arXiv 2017年

作者： Chen, Ge Duan, Xiaoming Mei, Wenjun Bullo, Francesco National Center for Mathematics and Interdisciplinary Sciences Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Mechanical Engineering Center of Control Dynamical-Systems and Computation University of California at Santa BarbaraCA93106-5070 United States

This paper studies linear stochastic approximation (SA) algorithms and their application to multi-agent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA algorithms to a deterministic or random final vector. We also characterize the system convergence rate, when the system is convergent. Moreover, differing from non-negative gain functions in traditional SA algorithms, this paper considers also the case when the gain functions are allowed to take arbitrary real numbers. Using our general treatment, we provide necessary and sufficient conditions to reach consensus and group consensus for first-order discrete-time multi-agent system over random signed networks and with state-dependent noise. Finally, we extend our results to the setting of multi-dimensional linear SA algorithms and characterize the behavior of the multi-dimensional Friedkin- Johnsen model over random interaction networks. Copyright © 2017, The Authors. All rights reserved.

关键词： Multi agent systems