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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

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

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

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

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

The meeting time of multiple random walks

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arXiv 2018年

作者： George, Mishel Patel, Rushabh Bullo, Francesco Mechanical Engineering University of California Santa BarbaraCA93106-5070 Northrop Grumman Aerospace Systems Redondo BeachCA Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA93106-5070

This article rigorously analyzes the meeting time between pursuers and evaders performing random walks on digraphs. There exist several bounds on the expected meeting time between random walkers on graphs in the literature, however, closed-form expressions are limited in scope. By utilizing the notion that multiple random walks on a common graph can be understood as a single random walk on the Kronecker product graph, we are able to provide the first analytic expression for the meeting time in terms of the transition matrices of the random walkers when modeled by either discrete-time Markov chains or continuous-time Markov chains. We further extend the results to the case of multiple pursuers and multiple evaders performing independent random walks. We present various sufficient conditions for pairs (or tuples) of transition matrices that satisfy certain conditions on the absorbing classes for which finite meeting times are guaranteed to *** Codes 60J10, 05C81, 05C50 Copyright © 2018, The Authors. All rights reserved.

关键词： Continuous time systems

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

Can we represent the depreobesity genetically?

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Obesity Medicine 2020年 19卷 100273-100273页

作者： Mediouni, Mohamed Bergantin, Leandro Bueno Madiouni, Riadh Kaczor-Urbanowicz, Karolina Elżbieta Urbanowicz, Andrzej 1420 Rue Laterrière Sherbrooke J1K 2R2 QC Canada Department of Pharmacology Universidade Federal de São Paulo Brazil University of Paris-Est Créteil Vitry sur Seine France Center for Oral and Head/Neck Oncology Research UCLA Section of Oral Biology Division of Oral Biology & Medicine Center for the Health Sciences UCLA School of Dentistry University of California at Los Angeles 10833 Le Conte Ave Box 951668 Los Angeles 90095-1668 CA United States UCLA Institute for Quantitative and Computational Biosciences University of California at Los Angeles 611 Charles E. Young Drive Boyer Hall 570 Box 951570 Los Angeles 90095-1606 CA United States Institute of Control and Computation Engineering Warsaw University of Technology Ul. Nowowiejska 15/19 Warsaw 00-665 Poland

Obesity and depression are serious public health problems and cause death in the world. In this article, we will study the concept of depreobesity that explains the depression in the context of obesity and vice versa. We will review whether animals can be used to understand the interrelationship between obesity and depression. We will propose saliva as a translational paradigm to predict the depreobesity. Policymakers need to identify new strategies for depreobesity by understanding the complexity of shared biology (depression-obesity). Perspectives for the future are promising. © 2020 Elsevier Ltd

关键词： Depreobesity Depression Genes Obesity Saliva