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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

Absolute Stabilization of Lur'e systems Under Event-Triggered Feedback

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IFAC-PapersOnLine 2017年第1期50卷 15301-15306页

作者： Zhang, Fan Mazo, Manuel van de Wouw, Nathan Delft Center for Systems and Control Delft University of Technology Netherlands Department of Mechanical Engineering Eindhoven University of Technology Netherlands Department of Civil Environmental and Geo-Engineering University of Minnesota United States

In this paper, we deal with event-triggered feedback control for Lur'e systems that consist of negative feedback interconnection of nominal linear dynamics and an unknown static nonlinearity. The unknown nonlinearity is conventionally assumed to lie in a given sector while the sector bounds are known. In the presence of event-triggered feedback mechanisms, the control input is only computed and updated when a specific event occurs. In this sense, control system resources (e.g. computation and communication capabilities) can be saved. A sufficient condition for the existence of an event-triggering condition and the corresponding even-triggered controller design are obtained by means of linear matrix inequality techniques. In addition, the avoidance of Zeno behavior is guaranteed. Furthermore, a result on the event-triggered emulation of a continuous-time feedback controller for Lur'e systems is presented. Finally, numerical simulations are given to illustrate the theoretical results along with some concluding remarks. © 2017

关键词： controllers Continuous time systems Feedback control Linear matrix inequalities Robustness (control systems) Stabilization Communication capabilities Event triggered Feedback interconnection Feedback mechanisms Linear matrix inequality techniques Lur'e systems Static non linearity Zeno behavior

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

Keynote address III: Recovery of function in major spinal cord injury using learning-guided spinal stimulation

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Keynote address III: Recovery of function in major spinal co...

NASA/ESA Conference on Adaptive Hardware and systems (AHS)

作者： Joel W. Burdick Mechanical Engineering Control & Dynamical Systems California Institute of Technology Pasadena CA 91125

ISBN: (纸本)9781538634400

Approximately 5,000,000 worldwide suffer from a serious spinal cord injury (SCI). Not only do the injured lose the ability to stand and walk (and sometimes move their arms), they suffer from additional injury-induced complications including loss of bladder and bowel control, decreased cardiovascular and pulmonary health, inability to regulate body temperature, and loss of muscle strength and bone density. The totality of the injury and its secondary dysfunctions makes daily activities of living a challenge. Because the median age of SCI in the U.S. is 32 years, SCI individuals amass an additional $1.4–$4.2 million in healthcare costs over their lifetimes. A team of researchers at Caltech, UCLA, and Univ. of Louisville have been developing new technologies and new therapies for motor complete SCI patients — those who have lost motor control below the level of their injury. The centerpiece of this approach is a multi-electrode array that is implanted over the lumbosacral spinal cord either in in the epidural space between the dura and the interior of the vertebral canal, or on the skin over this area. When this technology is coupled with locomotor training and drug therapy (when possible), SCI patients receiving this therapy can stand independently and make some voluntary movements (after being in a wheel chair for over 3 years). More importantly, they can expect to make useful gains in cardiovascular health, muscle tone, as well as improved autonomic function such as bladder, bowel, blood pressure, and temperature regulation. After first reviewing our clinical successes, this talk will focus on current research on new machine algorithms for automated tuning of the stimuli parameters.

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The Peregrine breather on the zero-background limit as the two-Soliton degenerate solution: An experimental study

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arXiv 2020年

作者： Chabchoub, Amin Slunyaev, Alexey Hoffmann, Norbert Dias, Frédéric Kibler, Bertrand Genty, Goëry Dudley, John M. Akhmediev, Nail Centre for Wind Waves and Water School of Civil Engineering University of Sydney SydneyNSW2006 Australia Marine Studies Institute University of Sydney SydneyNSW2006 Australia Department of Nonlinear Geophysical Processes Institute of Applied Physics RAS Nizhny Novgorod Russia Laboratory of Dynamical Systems and Applications National Research University Higher School of Economics Nizhny Novgorod Russia Dynamics Group Hamburg University of Technology Hamburg21073 Germany Department of Mechanical Engineering Imperial College London LondonSW7 2AZ United Kingdom School of Mathematics and Statistics University College Dublin Dublin Ireland Université Paris-Saclay ENS Paris-Saclay CNRS Centre Borelli Gif-sur-Yvette91190 France UMR 6303 CNRS-Université Bourgogne Franche-Comté Dijon21078 France Photonics Laboratory Physics Unit Tampere University Tampere33014 Finland Institut FEMTO-ST Université Bourgogne Franche-Comté CNRS UMR 6174 Besançon France Department of Theoretical Physics Research School of Physics Australian National University CanberraACT2600 Australia

Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schrödinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics. © 2020, CC-BY.

关键词： Solitons

Footstep and motion planning in semi-unstructured environments using randomized possibility graphs

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Footstep and motion planning in semi-unstructured environmen...

IEEE International Conference on Robotics and Automation (ICRA)

作者： Michael X. Grey Aaron D. Ames C. Karen Liu School of Interactive Computing Georgia Institute of Technology Atlanta GA Mechanical and Civil Engineering & Control and Dynamical Systems California Institute of Technology Pasadena CA

Traversing environments with arbitrary obstacles poses significant challenges for bipedal robots. In some cases, whole body motions may be necessary to maneuver around an obstacle, but most existing footstep planners can only select from a discrete set of predetermined footstep actions; they are unable to utilize the continuum of whole body motion that is truly available to the robot platform. Existing motion planners that can utilize whole body motion tend to struggle with the complexity of large-scale problems. We introduce a planning method, called the “Randomized Possibility Graph”, which uses high-level approximations of constraint manifolds to rapidly explore the “possibility” of actions, thereby allowing lower-level motion planners to be utilized more efficiently. We demonstrate simulations of the method working in a variety of semi-unstructured environments. In this context, “semi-unstructured” means the walkable terrain is flat and even, but there are arbitrary 3D obstacles throughout the environment which may need to be stepped over or maneuvered around using whole body motions.

关键词： Manifolds Planning Navigation Legged locomotion Shape Three-dimensional displays

Reachable Sets of Hidden CPS Sensor Attacks: Analysis and Synthesis Tools

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IFAC-PapersOnLine 2017年第1期50卷 2088-2094页

作者： Murguia C. Wouw N.V.D. Ruths J. Singapore University of Technology and Design Center for Research in Cyber Security (iTrust) Singapore Eindhoven University of Technology Mechanical Engineering Department Delft Center for Systems and Control Delft University of Technology Department of Civil Environmental and Geo-Engineering University of Minnesota Eindhoven Delft Minneapolis Netherlands University of Texas at Dallas Departments of Mechanical and Systems Engineering United States

For given system dynamics, control structure, and fault/attack detection procedure, we provide mathematical tools–in terms of Linear Matrix Inequalities (LMIs)–for characterizing and minimizing the set of states that sensor attacks can induce in the system while keeping the alarm rate of the fault detector sufficiently close to its false alarm rate in the attack-free case. This quantifies the attack's potential impact when it is constrained to stay hidden from the detector. Simulation results are presented to illustrate the performance of our tools. © 2017

关键词： cyber physical systems model-based fault detectors reachable sets security stochastic systems

Synchronization of Kuramoto Oscillators via Cutset Projections

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arXiv 2017年

作者： Jafarpour, Saber Bullo, Francesco Mechanical Engineering Department Center of Control Dynamical-Systems and Computation UC Santa BarbaraCA93106-5070 United States

—Synchronization in coupled oscillators networks is a remarkable phenomenon of relevance in numerous fields. For Kuramoto oscillators the loss of synchronization is determined by a trade-off between coupling strength and oscillator heterogeneity. Despite extensive prior work, the existing sufficient conditions for synchronization are either very conservative or heuristic and approximate. Using a novel cutset projection operator, we propose a new family of sufficient synchronization conditions;these conditions rigorously identify the correct functional form of the trade-off between coupling strength and oscillator heterogeneity. To overcome the need to solve a nonconvex optimization problem, we then provide two explicit bounding methods, thereby obtaining (i) the best-known sufficient condition for unweighted graphs based on the 2-norm, and (ii) the first-known generally-applicable sufficient condition based on the ∞-norm. We conclude with a comparative study of our novel ∞-norm condition for specific topologies and IEEE test cases;for most IEEE test cases our new sufficient condition is one to two orders of magnitude more accurate than previous rigorous tests. Copyright © 2017, The Authors. All rights reserved.

关键词： Synchronization

Modelling and testing of a historic steel suspension footbridge in Ireland

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Modelling and testing of a historic steel suspension footbri...

作者： O’Donnell, Deirdre Wright, Robert O’Byrne, Michael Sadhu, Ayan Murphy, Fiona Edwards Cahill, Paul Kelliher, Denis Ghosh, Bidisha Schoefs, Franck Mathewson, Alan Popovici, Emanuel Pakrashi, Vikram Dynamical Systems and Risk Laboratory School of Mechanical and Materials Engineering University College Dublin Dublin Ireland Malachy Walsh and Partners Cork Ireland Department of Civil Engineering Lakehead University ON Canada Electrical and Electronic Engineering School of Engineering University College Cork Cork Ireland University College Cork Cork Ireland Department of Civil Engineering School of Engineering University College Cork Cork Ireland Department of Civil Structural and Environmental Engineering Trinity College Dublin Dublin Ireland LUNAM Université Université de Nantes-Ecole Centrale de Nantes CNRS GeM Institute for Research in Civil and Mechanical Engineering University of Nantes Nantes France Heterogeneous Systems Integration Group Microsystems Group Tyndall National Institute University College Cork Cork Ireland Embedded.Systems@UCC Group Electrical and Electronic Engineering School of Engineering University College Cork Cork Ireland

Daly’s Bridge is a historic steel suspension footbridge in Ireland, known locally as the ‘Shaky Bridge’ for its noticeable movement under pedestrian loading. Although there is concern regarding the performance of the structure, testing or modelling has not been carried out to date and inadequate information exists in relation to carrying out such analyses. In this paper, Daly’s Bridge is instrumented and tested for the first time and a model of the bridge is established and improved in the process. Apart from ambient vibration, excitation from traversing pedestrians and cyclists is considered. Video analysis of dynamic deflection, a wavelet-packet-based technique using acceleration responses and dynamic measurements from a cheap smartphone accelerometer application are used to identify and compare the natural frequency of the bridge. The work contributes to the evidence base of full-scale measurements from instrumenting and analysing responses of aging pedestrian bridges, highlighting the complexity, challenges, opportunities and limitations related to the varied levels of information available from disparate sources. The study also highlights the need to investigate to what extent cheap sensors can be successfully used as compared to their more expensive and sophisticated counterparts.

关键词： Footbridges