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Distributed formation maneuver control by manipulating the complex Laplacian [article]

Hector Garcia de Marina
2021 arXiv   pre-print
This paper proposes a novel maneuvering technique for the complex-Laplacian-based formation control.  ...  These collective motions can be exploited to solve problems such as the shaped consensus (the rendezvous with a particular shape), the enclosing of a target, or translations with controlled speed and heading  ...  Acknowledgements This work has been supported by the grant Atraccion de Talento with reference number 2019-T2/TIC-13503 cofunded by the Government of the Autonomous Community of Madrid, and it has been  ... 
arXiv:2009.07625v2 fatcat:fheqd24v2vbbvmmybwvjxcxenu

Distributed Formation Control of Multi-Agent Systems Using Complex Laplacian

Zhiyun Lin, Lili Wang, Zhimin Han, Minyue Fu
2014 IEEE Transactions on Automatic Control  
Moreover, we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest  ...  A new technique based on complex Laplacian is introduced to address the problems of which formation shapes specified by inter-agent relative positions can be formed and how they can be achieved with distributed  ...  First, the paper presents a systematic approach based on complex Laplacian for the formation shape control problem that is significant in the field.  ... 
doi:10.1109/tac.2014.2309031 fatcat:du4fk6fhizg7fntglfvwak4zom

Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints [article]

Gennadij Heidel, Venera Khoromskaia, Boris N. Khoromskij, Volker Schulz
2020 arXiv   pre-print
Numerical tests for the 2D and 3D control problems confirm the linear complexity scaling of the method in the univariate grid size n.  ...  function in a tensor-structured format.  ...  Numerical tests for the 2D and 3D control problems confirm the linear complexity scaling of the method in the univariate grid size n.  ... 
arXiv:1809.01971v3 fatcat:lsiwjhk4t5evhga66nxeg76e3a

Autonomous Vehicle Convoy Formation Control with Size/Shape Switching for Automated Highways

2020 International Journal of Engineering  
A control architecture consisting of four algorithms is proposed to handle formation size/shape switching. The closed-form control law is at the core of these algorithms.  ...  This paper considers the control problem of a vehicle convoy modeled with linear dynamics. The convoy formation requirement is presented in terms of a quadratic performance index to minimize.  ...  In some other cases, a safe formation control strategy scales the formation shape (by a size switching strategy).  ... 
doi:10.5829/ije.2020.33.11b.07 fatcat:bgntmuzqvnf3tnl5qipf2pujti

Self-organized emergence of folded protein-like network structures from geometric constraints

Nora Molkenthin, Steffen Mühle, Antonia S. J. S. Mey, Marc Timme, Yaakov Koby Levy
2020 PLoS ONE  
Specifically, the distribution of the number of interaction neighbors a unit (amino acid) has, the scaling of the structure's spatial extent with chain length, the eigenvalue spectrum and the scaling of  ...  protein geometries as available through the Protein Data Base.  ...  We propose an approach to further understand geometry and formation processes using a complex network framework.  ... 
doi:10.1371/journal.pone.0229230 pmid:32106258 pmcid:PMC7046222 fatcat:tjwj6k3kd5a73kh5ul3digexxq

Frame bit allocation for the H.264/AVC video coder via Cauchy-density-based rate and distortion models

N. Kamaci, Y. Altunbasak, R.M. Mersereau
2005 IEEE transactions on circuits and systems for video technology (Print)  
Based on the observation that a Cauchy density is more accurate in estimating the distribution of the ac coefficients than the traditional Laplacian density, rate and distortion models with improved accuracy  ...  Extensive analysis with carefully selected anchor video sequences demonstrates a 0.24-dB average peak signal-to-noise ratio (PSNR) improvement over the JM 8.4 rate control algorithm, and a 0.33-dB average  ...  Then we will compare the rate-estimation accuracy of the Cauchy-pdf-based entropy function with the Laplacian-pdf-based entropy function by encoding a wide range of video sequences. A.  ... 
doi:10.1109/tcsvt.2005.852400 fatcat:y7qjaxk2nff5dfljtewtie2sme

Tensor Method for Optimal Control Problems Constrained by Fractional 3D Elliptic Operator with Variable Coefficients [article]

Britta Schmitt, Boris N. Khoromskij, Venera Khoromskaia, Volker Schulz
2020 arXiv   pre-print
Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated PCG iteration in the univariate grid size n.  ...  This method reduces the numerical cost for solving the control problem to O(n log n) (plus the quadratic term O(n^2) with a small weight), which is superior to the approaches based on the traditional linear  ...  Our approach exhibits the linear complexity scaling in dimension, O(dn 2 ).  ... 
arXiv:2006.09314v2 fatcat:b2ndaq54qvgjrp7w2vyvhclvpq

Geometric constraints in protein folding [article]

Nora Molkenthin, Steffen Mühle, Antonia S J S Mey, Marc Timme
2018 arXiv   pre-print
Specifically, the distribution of the number of interaction neighbors a unit (amino acid) has, the scaling of the structure's spatial extent with chain length, the eigenvalue spectrum and the scaling of  ...  protein geometries as available through the Protein Data Base.  ...  Distribution and scaling of Laplacian eigenvalues Lastly we explore the scaling of the second largest eigenvalue of the graph Laplacian with in Fig. 6 and find that it grows with , approaching a saturation  ... 
arXiv:1812.09692v1 fatcat:dz2oilq4cfbwdla5n6up6i5bra

Metrics for Graph Comparison: A Practitioner's Guide [article]

Peter Wills, Francois G. Meyer
2019 arXiv   pre-print
Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa.  ...  We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view.  ...  Graph data frequently consists of 10 4 to 10 8 vertices, and so algorithms whose complexity scales quadratically with the size of the graph quickly become unfeasible.  ... 
arXiv:1904.07414v2 fatcat:3xhzagkrifhxpa3uisljivk4ce

A literature survey of matrix methods for data science [article]

Martin Stoll
2020 arXiv   pre-print
With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial role in enabling and improving data science computations with many new developments being fueled  ...  Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines.  ...  or account for the complexity and size of the data.  ... 
arXiv:1912.07896v2 fatcat:umml3cx7ofdhxlh5b5uexxpkxy

Metrics for graph comparison: A practitioner's guide

Peter Wills, François G. Meyer, Pin-Yu Chen
2020 PLoS ONE  
Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa.  ...  We make recommendations on the applicability of different distance measures to the analysis of empirical graph data based on this multi-scale view.  ...  Graph data frequently consists of 10 4 to 10 8 vertices, and so algorithms whose complexity scales quadratically with the size of the graph quickly become unfeasible.  ... 
doi:10.1371/journal.pone.0228728 pmid:32050004 pmcid:PMC7015405 fatcat:igitnxkvcrdotafcbex5kt75mq

A complex network based model for detecting isolated communities in water distribution networks

Nan Sheng, Youwei Jia, Zhao Xu, Siu-Lau Ho, Chi Wai Kan
2013 Chaos  
In this paper, we explore the formation of isolated communities in WDN based on complex network theory.  ...  Water distribution network (WDN) is a typical real-world complex network of major infrastructure that plays an important role in human's daily life.  ...  , spectral analysis based on Laplacian matrix can be a new and effective approach for fast and accurate detection of isolated communities.  ... 
doi:10.1063/1.4823803 pmid:24387541 fatcat:mvptntoh3jcuzn57dtfadyafke

Efficient embedding of complex networks to hyperbolic space via their Laplacian

Gregorio Alanis-Lobato, Pablo Mier, Miguel A. Andrade-Navarro
2016 Scientific Reports  
Here, a different strategy is followed in the form of the Laplacian-based Network Embedding, a simple yet accurate, efficient and data driven manifold learning approach, which allows for the quick geometric  ...  Current efforts to infer the hyperbolic geometry of complex networks bet for a Maximum Likelihood Estimation (MLE) approach, in which the space of PS models with the same structural properties as the network  ...  In addition, the posts published by Alex Kritchevsky and Arpan Saha on http://www.quora.com/ were very important for a clear and intuitive presentation of the Laplacian as an operator.  ... 
doi:10.1038/srep30108 pmid:27445157 pmcid:PMC4957117 fatcat:dpf47l4nvzdbbhgw25ltjfbrbe

Brain-Swarm Control Interfaces: The Transition from Controlling One Robot to a Swarm of Robots

Panagiotis Artemiadis
2017 Advances in Robotics & Automation  
Controlled through those interfaces is quite limited, i.e. only one or two in most cases.  ...  Recent advances in computing, sensing, actuation and control technologies are currently enabling the development of swarms of aerial vehicles, varying in complexity, size and overall scale [33, 34] .  ...  Currently, most large robotic systems are controlled by multiple operators, often via remote control. For larger systems with more agents, such an approach is not practical.  ... 
doi:10.4172/2168-9695.1000e127 fatcat:bqyj2bmhpbcppgmvgg44e5cvlq

Robust Image Retargeting via Axis-Aligned Deformation

Daniele Panozzo, Ofir Weber, Olga Sorkine
2012 Computer graphics forum (Print)  
We demonstrate how the image size and the saliency map can be changed in real time with our approach, and present results on various input images, including the RETARGETME benchmark.  ...  Thanks to the 1D parameterization, our method only requires solving a small quadratic program, which can be done within a few milliseconds on the CPU with no precomputation overhead.  ...  strength of Laplacian regularization and minimal grid cell size).  ... 
doi:10.1111/j.1467-8659.2012.03001.x fatcat:gthlrw732vf6jnrwdvviy4nbhi
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