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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

Synchronization of Kuramoto oscillators: Inverse Taylor expansions

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arXiv 2018年

作者： Jafarpour, Saber Huang, Elizabeth Y. Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara United States Department of Mechanical Engineering Center for Control Dynamical Systems and Computation University of California Santa Barbara United States

Synchronization in networks of coupled oscillators is a widely studied topic with extensive scientific and engineering applications. In this paper, we study the frequency synchronization problem for networks of Kuramoto oscillators with arbitrary topology and heterogeneous edge weights. We propose a novel equivalent transcription for the equilibrium synchronization equation. Using this transcription, we develop a power series expansion to compute the synchronized solution of the Kuramoto model as well as a sufficient condition for the strong convergence of this series expansion. Truncating the power series provides (i) an efficient approximation scheme for computing the synchronized solution, and (ii) a simple-to-check, statistically-correct hierarchy of increasingly accurate synchronization tests. This hierarchy of tests provides a theoretical foundation for and generalizes the best-known approximate synchronization test in the literature. Our numerical experiments illustrate the accuracy and the computational efficiency of the truncated series approximation compared to existing iterative methods and existing synchronization tests. Copyright © 2018, The Authors. All rights reserved.

关键词： Synchronization

Translational Model Identification and Robust control for the Parrot Mambo UAS Multicopter

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Translational Model Identification and Robust Control for th...

IEEE Globecom Workshops

作者： Ignacio Rubio Scola Gabriel Alexis Guijarro Reyes Luis Rodolfo Garcia Carrillo Joao Hespanha Junfei Xie FCEIA-UNR Rosario Argentina Texas A&M University Corpus Christi TX USA Center for Control Dynamical Systems and Computation University of California Santa Barbara CA USA Department of Electrical and Computer Engineering San Diego State University San Diego CA

ISBN: (数字)9781728109602

ISBN: (纸本)9781728109619

Two main problems are addressed in this paper. The first one is the model identification for a commercial unmanned aircraft system (UAS): the Parrot Mambo multicopter. The second one aims at synthesizing a robust controller for guaranteeing the stability of the X and Y translational dynamics of this UAS. To accomplish these goals, we first collect input-output data from a set of real-time flight experiments. Next, by applying an extended least square (ELS) algorithm to the data, a group of dynamic models are identified. Due to uncertainties, the obtained models are similar in nature but exhibit parametrical variations. For this reason, from the set of identified models, a unique nominal (i.e., average) parameter-dependent linear model is built, which also takes into account the minimum and maximum values defining the model parametrical variations. Finally, a static linear controller is synthesized for the dynamics of interest, guaranteeing global stability for every model. The identification results and the performance of the closed- loop controller are validated in a set of numerical simulations, demonstrating the effectiveness of the proposed modeling and control approaches.

关键词： Mathematical model Robust control Numerical models computational modeling Real-time systems Uncertainty Estimation

Markov chains with maximum return time entropy for robotic surveillance

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arXiv 2018年

作者： Duan, Xiaoming George, Mishel Bullo, Francesco Mechanical Engineering Department Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States

Motivated by robotic surveillance applications, this paper studies the novel problem of maximizing the return time entropy of a Markov chain, subject to a graph topology with travel times and stationary distribution. The return time entropy is the weighted average, over all graph nodes, of the entropy of the first return times of the Markov chain;this objective function is a function series that does not admit in general a closed form. The paper features theoretical and computational contributions. First, we obtain a discrete-time delayed linear system for the return time probability distribution and establish its convergence properties. We show that the objective function is continuous over a compact set and therefore admits a global maximum;a unique globally-optimal solution is known only for complete graphs with unitary travel times. We then establish upper and lower bounds between the return time entropy and the well-known entropy rate of the Markov chain. To compute the optimal Markov chain numerically, we establish the asymptotic equality between entropy, conditional entropy and truncated entropy, and propose an iteration to compute the gradient of the truncated entropy. Finally, we apply these results to the robotic surveillance problem. Our numerical results show that, for a model of rational intruder over prototypical graph topologies and test cases, the maximum return time entropy chain performs better than several existing Markov chains. Copyright © 2018, The Authors. All rights reserved.

关键词： Linear systems

Synchronization of coupled oscillators: The taylor expansion of the inverse kuramoto map

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arXiv 2018年

作者： Huang, Elizabeth Y. Jafarpour, Saber Bullo, Francesco Department of Mechanical Engineering Center of Control Dynamical Systems and Computation University of California Santa Barbara93106-5070 United States

Synchronization in the networks of coupled oscillators is a widely studied topic in different areas. It is well-known that synchronization occurs if the connectivity of the network dominates heterogeneity of the oscillators. Despite extensive study on this topic, the quest for sharp closed-form synchronization tests is still in vain. In this paper, we present an algorithm for finding the Taylor expansion of the inverse Kuramoto map. We show that this Taylor series can be used to obtain a hierarchy of increasingly accurate approximate tests with low computational complexity. These approximate tests are then used to estimate the threshold of synchronization as well as the position of the synchronization manifold of the network. Copyright © 2018, The Authors. All rights reserved.

关键词： Synchronization

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

Time-domain multiplexed 2-dimensional cluster state: Universal quantum computing platform

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arXiv 2019年

作者： Asavanant, Warit Shiozawa, Yu Yokoyama, Shota Charoensombutamon, Baramee Emura, Hiroki Alexander, Rafael N. Takeda, Shuntaro Yoshikawa, Jun-ichi Menicucci, Nicolas C. Yonezawa, Hidehiro Furusawa, Akira Department of Applied Physics School of Engineering University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Centre for Quantum Computation and Communication Technology School of Engineering and Information Technology University of New South Wales CanberraACT2600 Australia Center for Quantum Information and Control University of New Mexico MSC07-4220 AlbuquerqueNM87131-0001 United States Centre for Quantum Computation and Communication Technology School of Science RMIT University MelbourneVIC3001 Australia

Quantum computation promises applications1-3that are thought to be impossible with classical computation. To realize practical quantum computation, the following three properties will be necessary: universality, scalability, and fault-tolerance. Universality is the ability to execute arbitrary multi-input quantum algorithms. Scalability means that computational resources such as logical qubits can be increased without requiring exponential increase in physical resources. Lastly, fault-tolerance is the ability to perform quantum algorithms in presence of imperfections and noise. A promising approach to scalability was demonstrated with the generation of onemillion-mode 1-dimensional cluster state3, a resource for one-input computation in measurement-based quantum computation (MBQC)5,6. The demonstration was based on time-domain multiplexing (TDM) approach2,4,8using continuous-variable (CV) optical flying qumodes (CV analogue of qubit). Demonstrating universality, however, has been a challenging task for any physical system and approach. Here, we present, for the first time among any physical system, experimental realization of a scalable resource state for universal MBQC: a 2-dimensional cluster state. We also prove the universality and give the methodology for utilizing this state in MBQC. Our state is based on TDM approach that allows unlimited resource generation regardless of the coherence time of the system. As a demonstration of our method, we generate and verify a 2-dimensional cluster state capable of about 5,000 operation steps on 5 inputs. Note that there are no limitation on the number of operation steps, and the number of inputs can be increased by several orders of magnitude with current technology10,11. Furthermore, by increasing the squeezing level, fault-tolerance can also be achieved by combining our method with error correction schemes for CV cluster states12,13. Thus, our work not only achieves scalable generation of resource for universal MBQC, bu

关键词： Fault tolerance

Distributed Resource Allocation through Utility Design – Part I: Optimizing the Performance Certificates via the Price of Anarchy

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arXiv 2018年

作者： Paccagnan, Dario Chandan, Rahul Marden, Jason R. Mechanical Engineering Department Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States Department of Electrical and Computer Engineering University of California Santa BarbaraCA93106-5070 United States

—Game theory has emerged as a fruitful paradigm for the design of networked multiagent systems. A fundamental component of this approach is the design of agents’ local utility functions so that their self-interested maximization results in a desirable collective behavior. In this work we focus on a well-studied class of distributed resource allocation problems where each agent is requested to select a subset of resources with the goal of optimizing a given system-level objective, separable over the resources. Our core contribution is the development of a novel framework to tightly characterize the worst case performance of any resulting Nash equilibrium (price of anarchy) as a function of the chosen agents’ utility functions. Leveraging this result, we then identify how to design such utilities so as to optimize the price of anarchy through a tractable linear program. This provides us with a-priori performance certificates applicable to any existing learning algorithm capable of driving the system to an equilibrium. Part II of this work specializes these results to submodular and supermodular objectives, discusses the complexity of computing Nash equilibria, and provides multiple illustrations of the theoretical findings. Copyright © 2018, The Authors. All rights reserved.

关键词： Game theory

Distributed resource allocation through utility design - Part II: Applications to submodular, supermodular and set covering problems

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arXiv 2018年

作者： Paccagnan, Dario Marden, Jason R. Mechanical Engineering Department Center of Control Dynamical Systems and Computation UC Santa Barbara CA93106-5070 United States Department of Electrical and Computer Engineering University of California Santa BarbaraCA93106-5070 United States

A fundamental component of the game theoretic approach to distributed control is the design of local utility functions. In Part I of this work we showed how to systematically design local utilities so as to maximize the induced worst case performance. The purpose of the present manuscript is to specialize the general results obtained in Part I to a class of monotone submodular, supermodular and set covering problems. In the case of set covering problems, we show how any distributed algorithm capable of computing a Nash equilibrium inherits a performance certificate matching the well known 1 - 1=e approximation of [1]. Relative to the class of submodular maximization problems considered here, we show how the performance offered by the game theoretic approach improves on existing approximation algorithms. We briefly discuss the algorithmic complexity of computing (pure) Nash equilibria and show how our approach generalizes and subsumes previously fragmented results in the area of optimal utility design. Two applications and corresponding numerics are presented: the vehicle target assignment problem and a coverage problem arising in distributed caching for wireless networks. Copyright © 2018, The Authors. All rights reserved.

关键词： Combinatorial optimization