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Multiple-node basin stability in complex dynamical networks

Physical Review E 2017年第3期95卷 032317-032317页

作者： Chiranjit Mitra Anshul Choudhary Sudeshna Sinha Jürgen Kurths Reik V. Donner Potsdam Institute for Climate Impact Research Research Domain IV–Transdisciplinary Concepts & Methods 14412 Potsdam Germany Humboldt University of Berlin Department of Physics 12489 Berlin Germany Indian Institute of Science Education and Research (IISER) Mohali Knowledge City SAS Nagar Sector 81 Manauli P.O. 140 306 Punjab India University of Aberdeen Institute for Complex Systems and Mathematical Biology Aberdeen AB24 3UE United Kingdom Nizhny Novgorod State University Department of Control Theory Nizhny Novgorod 606950 Russia

Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world networked dynamical systems such as ecosystems, power grids, the human brain, etc. This necessitates the development of appropriate quantifiers of stability of multiple stable states of such systems. Motivated by the concept of basin stability (BS) [P. J. Menck et al., Nat. Phys. 9, 89 (2013)], we propose here the general framework of multiple-node basin stability for gauging the global stability and robustness of networked dynamical systems in response to nonlocal perturbations simultaneously affecting multiple nodes of a system. The framework of multiple-node BS provides an estimate of the critical number of nodes that, when simultaneously perturbed, significantly reduce the capacity of the system to return to the desired stable state. Further, this methodology can be applied to estimate the minimum number of nodes of the network to be controlled or safeguarded from external perturbations to ensure proper operation of the system. Multiple-node BS can also be utilized for probing the influence of spatially localized perturbations or targeted attacks to specific parts of a network. We demonstrate the potential of multiple-node BS in assessing the stability of the synchronized state in a deterministic scale-free network of Rössler oscillators and a conceptual model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics.

关键词： Attacks on networks Cascades Chaos Classical mechanics Collective behavior in networks Collective dynamics Complex systems control & applications of chaos Coupled oscillators Dynamics of networks Mathematical physics Network resilience Network stability Network structure Robustness Self-organized systems Synchronization

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Reduced-Order Modeling of Index-1 Vibrational systems Using Interpolatory Projections

Reduced-Order Modeling of Index-1 Vibrational Systems Using ...

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International Conference on Computer and Information Technology

作者： Peter Benner Jens Saak M. Monir Uddin Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstra?e 1 D-39106 Magdeburg Germany Department of Mathematics and Physics North South University 15/B Bashundhara Dhaka-1239 Bangladesh

ISBN: (纸本)9781509040919

Large sparse second order index-1 descriptor systems arise in various disciplines of science and engineering, such as constraint mechanics or multibody dynamics, mechatronics (where mechanical and electrical elements are coupled), but also RLC circuit design. Simulation, controller design and design optimization are only some applications of such models. Either of these tasks, just like any other many-query situation becomes unfeasible when the system is high dimensional. This paper discusses an algorithm to obtain a reduced state space model of a large sparse second order index-1 system using an interpolatory projection method based on the iterative rational Krylov algorithm (IRKA). In each iteration of this algorithm, we need to solve a number of linear systems. The main contribution of this paper is to solve these linear systems by exploiting the sparsity of the original model, which reduces the computational cost drastically. The algorithm is applied to a micro-mechanical piezo-actuated structural FEM model of a certain building block of a machine tool. Numerical experiments with a complex 3d model of an adaptive spindle support (a piezo-mechanical multiphysics system) show the effectivity and efficiency of the techniques.

关键词： second order index-1 systems sparsity model reduction interpolatory projections

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Adjoint-Based Optimal Boundary control of a Stefan Problem System Fully Coupled with Navier-Stokes Equations

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PAMM 2016年第1期16卷

作者： Björn Baran Jan Heiland Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg

Free boundary and moving boundary problems, that can be used to model crystal growth or the solidification and melting of pure materials, receive growing attention in science and technology. The optimal control of these problems appear even more interesting since certain desired shapes of the boundaries improve, e.g., the material quality in the case of crystal growth. We consider the so called two-phase Stefan problem that models a solid and a liquid phase separated by a moving interface. In the work presented, we take a sharp interface model approach and define a quadratic tracking-type cost functional that penalizes the deviation of the interface from the desired state at a final time as well as the control costs. Following the “optimize-then-discretize” paradigm, we formulate a first order optimality system using the formal Lagrange approach and derive the adjoint PDE system that provides the needed gradient of the cost functional. By means of an example setup of a container with an in- and outflow of water and a cooling unit at the bottom, we illustrate how the derived formulations can be used to achieve a desired interface between the solid and the fluid phase by controlling the flow at the inlet. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Numerical solution to low rank perturbed Lyapunov equations by the sign function method

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PAMM 2016年第1期16卷

作者： Peter Benner Jonas Denißen Max Planck Institute for Dynamics of Complex Technical Systems Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg Germany

We investigate the numerical solution to a low rank perturbed Lyapunov equation A T X + XA = W via the sign function method (SFM). The sign function method has been proposed to solve Lyapunov equations, see e.g. [1], but here we focus on a framework where the matrix A has a special structure, i. e. A = B + UCV T , where B is a blockdiagonal matrix and UCV T is a low rank perturbation. We show that this structure can be kept throughout the sign function iteration but the rank of the perturbation doubles per iteration. Therefore, we apply a low rank approximation to the perturbation in order to keep its numerical rank small. We compare the standard SFM with its structure preserving variant presented in this paper by means of numerical examples from viscously damped mechanical systems. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Solving Differential Matrix Equations using Parareal

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PAMM 2016年第1期16卷

作者： Martin Köhler Norman Lang Jens Saak Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Computational Methods in Systems and Control Theory Technische Universität Chemnitz Faculty of Mathematics

Differential matrix equations appear in many applications like optimal control of partial differential equations, balanced truncation model order reduction of linear time varying systems and many more. Here, we will focus on differential Riccati equations (DRE). Solving such matrix-valued ordinary differential equations (ODE) is a highly time consuming process. We present a Parareal based algorithm applied to Rosenbrock methods for the solution of the matrix-valued differential Riccati equations. Considering problems of moderate size, direct matrix equation solvers for the solution of the algebraic Lyapunov equations arising inside the time intgration methods are used. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Distributed optimal control problems governed by coupled convection dominated PDEs with control constraints

Lecture Notes in Computational Science and Engineering

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Lecture Notes in computational Science and Engineering 2015年 103卷 469-478页

作者： Yücel, Hamdullah Benner, Peter Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

We study the numerical solution of control constrained optimal control problems governed by a system of convection diffusion equations with nonlinear reaction terms, arising from chemical processes. control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method or by adding a Moreau-Yosida-type penalty function to the cost functional. An adaptive mesh refinement indicated by a posteriori error estimates is applied for both approaches. © Springer International Publishing Switzerland 2015.

关键词： Optimal control systems

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26th Annual computational Neuroscience Meeting (CNS*2017) of the Organization for computational Neuroscience Antwerp, Belgium, July 15-20, 2017

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BMC NEUROSCIENCE 2017年第SUPPL 1期18卷 59-59页

作者： [Anonymous] Indiana University Purdue University Indianapolis Indianapolis IN 46032 USA Stark Neurosciences Research Institute Indiana University School of Medicine Indianapolis IN 46032 USA Department of Mathematics East Carolina University Greenville NC 27858 USA Jülich Supercomputing Centre Forschungszentrum Jülich 52425 Jülich Germany Future Systems Swiss National Supercomputing Centre 8092 Zurich Switzerland User Engagement and Support Swiss National Supercomputing Centre 6900 Lugano Switzerland Institut de Neurosciences des Systèmes Aix Marseille Univ 13005 Marseille France Simulation Lab Neuroscience Forschungszentrum Jülich Jülich Germany Department of Experimental Psychology Ghent University 9000 Ghent Belgium Donders Center for Cognitive Neuroimaging Radboud University 6525HR Nijmegen The Netherlands Department of Electrical Computer and Energy Engineering University of Colorado Boulder CO 80309 USA Department of Neurosurgery Johns Hopkins School of Medicine Baltimore MD 21287 USA Department of Neurology Johns Hopkins School of Medicine Baltimore MD 21287 USA Department of Otolaryngology Johns Hopkins School of Medicine Baltimore MD 21287 USA INSERM U968 Paris France Sorbonne Universités UPMC University Paris 06 UMR_S 968 Institut de la Vision Paris France CNRS UMR_7210 Paris France Department of Computer Architecture and Technology University of Granada (CITIC) Granada Spain Sorbonne Universités UPMC Univ Paris 06 INSERM CNRS Institut de la Vision Paris France Department of Adaptive Machine Systems Osaka University Osaka Japan Department of Computer Science University of Cergy-Pontoise Cergy-Pontoise France Department of Physics and Astronomy College of Charleston Charleston SC 29424 USA School of Physics Faculty of Science University of Sydney Sydney NSW 2006 Australia Center of Excellence for Integrative Brain Function Australian Research Council Sydney Australia Max Planck Institute for Human Cognitive and Brain Sciences Saxony Lei

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26th Annual computational Neuroscience Meeting (CNS*2017): Part 3 Antwerp, Belgium. 15-20 July 2017 Abstracts

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BMC NEUROSCIENCE 2017年第SUPPL 1期18卷 95-176页

作者： [Anonymous] Department of Neuroscience Yale University New Haven CT 06520 USA Department Physiology & Pharmacology SUNY Downstate Brooklyn NY 11203 USA NYU School of Engineering 6 MetroTech Center Brooklyn NY 11201 USA Departament de Matemàtica Aplicada Universitat Politècnica de Catalunya Barcelona 08028 Spain Institut de Neurobiologie de la Méditerrannée (INMED) INSERM UMR901 Aix-Marseille Univ Marseille France Center of Neural Science New York University New York NY USA Aix-Marseille Univ INSERM INS Inst Neurosci Syst Marseille France Laboratoire de Physique Théorique et Modélisation CNRS UMR 8089 Université de Cergy-Pontoise 95300 Cergy-Pontoise Cedex France Department of Mathematics and Computer Science ENSAT Abdelmalek Essaadi’s University Tangier Morocco Laboratory of Natural Computation Department of Information and Electrical Engineering and Applied Mathematics University of Salerno 84084 Fisciano SA Italy Department of Medicine University of Salerno 84083 Lancusi SA Italy Dipartimento di Fisica Università degli Studi Aldo Moro Bari and INFN Sezione Di Bari Italy Data Analysis Department Ghent University Ghent Belgium Coma Science Group University of Liège Liège Belgium Cruces Hospital and Ikerbasque Research Center Bilbao Spain BIOtech Department of Industrial Engineering University of Trento and IRCS-PAT FBK 38010 Trento Italy Department of Data Analysis Ghent University Ghent 9000 Belgium The Wellcome Trust Centre for Neuroimaging University College London London WC1N 3BG UK Department of Electronic Engineering NED University of Engineering and Technology Karachi Pakistan Blue Brain Project École Polytechnique Fédérale de Lausanne Lausanne Switzerland Departement of Mathematics Swansea University Swansea Wales UK Laboratory for Topology and Neuroscience at the Brain Mind Institute École polytechnique fédérale de Lausanne Lausanne Switzerland Institute of Mathematics University of Aberdeen Aberdeen Scotland UK Department of Integrativ

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On the state estimation problem for discrete ensembles from discrete-time output snapshots

On the state estimation problem for discrete ensembles from ...

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American control Conference

作者： Shen Zeng Hideaki Ishii Frank Allgower Institute for Systems Theory and Automatic Control University of Stuttgart 70550 Stuttgart Germany Department of Computational Intelligence and Systems Science Tokyo Institute of Technology Japan

ISBN: (纸本)9781479917730

We consider the problem of reconstructing the initial states of a group of structurally identical LTI systems in the situation that output measurements of the individual systems in the group are received at discrete time steps and in an anonymized manner: While we do know all output measurements of the individual systems in the group, we do not know which output measurement corresponds to which system. This specific state estimation problem is motivated by emerging problems in applied fields that are dealing with populations of structurally identical systems for which it is only possible to measure the population as a whole, e.g. due to economic or technological reasons. We adopt a measure theoretical approach in which the group is modelled by an LTI system describing the structure of the individual systems and an initial state which is expressed by a discrete measure. We derive characterizations for the state estimation to admit a unique solution.

关键词： State estimation discrete-time individual system LTI Snapshots Ensembles Output INITIAL CONDITIONS

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Sampled Observability of Discrete Heterogeneous Ensembles from Anonymized Output Measurements

Sampled Observability of Discrete Heterogeneous Ensembles fr...

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IEEE Annual Conference on Decision and control

ISBN: (纸本)9781479978878

We consider the problem of reconstructing the initial states of a group of heterogeneous LTI systems in the situation that output measurements of the subsystems are received at discrete time steps and in an anonymized manner. By the latter we refer to the fact that in each time step, the association of the output measurements of the subsystems and the subsystem that produced it is lost. Therefore, the output measurements at a given time step are called output snapshot, as they capture only the group's outputs as a whole. This setup is motivated by state estimation problems for populations of dynamical systems in which the output measurements of the subsystems are only given as statistics. We give a theoretical result concerning the number of measurement times needed in order to be able to uniquely reconstruct the initial states, and furthermore illustrate a practical method for state estimation under noisy output snapshots.

关键词： SUB-SYSTEM State estimation Output Snapshots Observability discrete-time Ensembles practical methods DYNAMICAL systems

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