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88th Annual Meeting on the International Association of Applied Mathematics and Mechanics, GAMM 2017

作者： Baran, Björn Benner, Peter Heiland, Jan Saak, Jens Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

Problems featuring moving interfaces appear in many applications. They can model solidification and melting of pure materials, crystal growth and other multi-phase problems. The control of the moving interface enables to, for example, influence production processes and, thus, the product material quality. We consider the two-phase Stefan problem that models a solid and a liquid phase separated by the moving interface. In the liquid phase, the heat distribution is characterized by a convection-diffusion equation. The fluid flow in the liquid phase is described by the Navier–Stokes equations which introduces a differential algebraic structure to the system. The interface movement is coupled with the temperature through the Stefan condition, which adds additional algebraic constraints. Our formulation uses a sharp interface representation and we define a quadratic tracking-type cost functional as a target of a control input. We compute an open loop optimal control for the Stefan problem using an adjoint system. For a feedback representation, we linearize the system about the trajectory defined by the open loop control. This results in a linear-quadratic regulator problem, for which we formulate the differential Riccati equation with time varying coefficients. This Riccati equation defines the corresponding feedback gain. Further, we present the feedback formulation that takes into account the structure and the differential algebraic components of the problem. Also, we discuss how the complexities that come, for example, with mesh movements, can be handled in a feedback setting. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

关键词： Feedback

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Synchronization and aggregation of nonlinear power systems with consideration of bus network structures

arXiv

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arXiv 2018年

作者： Mlinarić, Petar Ishizaki, Takayuki Chakrabortty, Aranya Grundel, Sara Benner, Peter Imura, Jun-Ichi Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39106 Germany Department of Systems and Control Engineering School of Engineering Tokyo Institute of Technology 2-12-1 Meguro Tokyo Japan Electrical & Computer Engineering North Carolina State University RaleighNC27695

We study nonlinear power systems consisting of generators, generator buses, and non-generator buses. First, looking at a generator and its bus' variables jointly, we introduce a synchronization concept for a pair of such joint generators and buses. We show that this concept is related to graph symmetry. Next, we extend, in two ways, the synchronization from a pair to a partition of all generators in the networks and show that they are related to either graph symmetry or equitable partitions. Finally, we show how an exact reduced model can be obtained by aggregating the generators and associated buses in the network when the original system is synchronized with respect to a partition, provided that the initial condition respects the partition. Additionally, the aggregation-based reduced model is again a power *** Codes 93A15, 93C10, 94C15 Copyright © 2018, The Authors. All rights reserved.

关键词： Synchronization

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Inexact methods for the low rank solution to large scale Lyapunov equations

arXiv

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arXiv 2018年

作者： Kürschner, Patrick Freitag, Melina A. Max Planck Institute for Dynamics of Complex Technical Systems Computational Methods in Systems and Control Theory Magdeburg Germany Department of Mathematical Sciences University of Bath Claverton Down BA2 7AY United Kingdom

The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit (LR-ADI) iteration are established numerical tools for computing low-rank solution factors of large-scale Lyapunov equations. In order to generate the basis vectors for the RKSM, or extend the low-rank factors within the LR-ADI method the repeated solution to a shifted linear system is necessary. For very large systems this solve is usually implemented using iterative methods, leading to inexact solves within this inner iteration. We derive theory for a relaxation strategy within these inexact solves, both for the RKSM and the LR-ADI method. Practical choices for relaxing the solution tolerance within the inner linear system are then provided. The theory is supported by several numerical examples.65F10, 65F30 Copyright © 2018, The Authors. All rights reserved.

关键词： Lyapunov functions

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Technology of flood water zones moddeling in downstream pool of hydroelectric power station at strong flow through its water abstraction points

Technology of flood water zones moddeling in downstream pool...

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2017 All-Russian Conference "Spatial Data Processing for Monitoring of Natural and Anthropogenic Processes, SDM 2017

作者： Gachenko, Andrey S. Hmelnov, Alexei E. Abasov, Nikolay V. Osipchuk, Evgeny N. Matrosov Institute for System Dynamics and Control Theory SB RAS Irkutsk Russia Melentiev Energy Systems Institute Russian Academy of Sciences Siberian Branch Irkutsk Russia

The article provides a technology for estimating of potential flooding areas in the lower pool of the Irkutsk HPP at high mandatory water flow expenses through its water abstraction points, that probability has increased significantly since 2001, following the adoption by the Government of Russian Federation of a decree on strict control limits of Lake Baikal level within 456-457 m (in Pacific reference system). The article offers investigation on structure and method of digital modeling of the relief of the Angara river within 67 km in conditions of limited information (inaccuracy of the underwater and above-water relief).

关键词： Hydroelectric power plants

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Extremum Seeking for Time-Varying Functions using Lie Bracket Approximations

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IFAC-PapersOnLine 2017年第1期50卷 5522-5528页

作者： Grushkovskaya V. Dürr H.-B. Ebenbauer C. Zuyev A. Institute for Systems Theory and Automatic Control University of Stuttgart Stuttgart 70569 Germany Institute of Applied Mathematics and Mechanics National Academy of Sciences of Ukraine Sloviansk 84100 Ukraine Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg 39106 Germany

The paper presents a control algorithm that steers a system to an extremum point of a time-varying function. The proposed extremum seeking law depends on values of the cost function only and can be implemented without knowing analytical expression of this function. By extending the Lie brackets approximation method, we prove the local and semi-global practical uniform asymptotic stability for time-varying extremum seeking problems. For this purpose, we consider an auxiliary non-autonomous system of differential equations and propose asymptotic stability conditions for a family of invariant sets. The obtained control algorithm ensures the motion of a system in a neighborhood of the curve where the cost function takes its minimal values. The dependence of the radius of this neighborhood on the bounds of the derivative of a time-varying function is shown. © 2017

关键词： adaptive control extremum seeking Lyapunov methods non-autonomous systems stability of nonlinear systems

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Multi-Agent Approach for Dynamic Elasticity of Virtual Machines Provisioning in Heterogeneous Distributed Computing Environment

Multi-Agent Approach for Dynamic Elasticity of Virtual Machi...

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International Conference on High Performance Computing & Simulation (HPCS)

作者： Alexander Feoktistov Ivan Sidorov Andrei Tchernykh Alexei Edelev Valery Zorkalzev Roman Kostromin Sergey Gorsky Igor Bychkov Arutyun Avetisyan Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences Irkutsk Russia Matrosov Inst. for Syst. Dynamics & Control Theor. Irkutsk Russia Ivannikov Institute for System Programming of the Russian Academy of Sciences Moscow Russia Melentiev Energy Systems Institute of the Siberian Branch of the Russian Academy of Sciences Irkutsk Russia

ISBN: (纸本)9781538678800

We address dynamic elasticity issues of VM provisioning in a heterogeneous distributed computing environment that integrates resources of a data center. We consider the scenario when the center includes dedicated resources (private cloud) for providing virtualized service and non-dedicated resources for Grid-computing. Existing platforms for the resource virtualization does not support management of such an infrastructure. We propose an approach to a job management based on the dynamic elasticity of virtual machines provisioning using resources of both types. We develop the multi¬agent job scheduler for dedicated resources and hypervisor shell to launch virtual machines through queues of resource management systems in non-dedicated resources. The scheduler provides a dynamic elasticity of virtual machine provisioning. Advantages of the offered approach to the resource virtualization are demonstrated by an example of a job flow management for a scalable application to solve the complicated practical problem. It is related to the energy security of Vietnam. Provided experiments show that using the developed tools together with the platform for the resource virtualization enables agents to significantly speed up the problem-solving process.

关键词： Cloud computing Resource management Dynamic scheduling Virtual machine monitors Elasticity Virtual machining

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Obstacle Avoidance Problem for Driftless Nonlinear systems with Oscillating controls

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IFAC-PapersOnLine 2017年第1期50卷 10476-10481页

作者： Zuyev A. Grushkovskaya V. Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg 39106 Germany Institute of Applied Mathematics and Mechanics National Academy of Sciences of Ukraine Sloviansk 84100 Ukraine Institute for Systems Theory and Automatic Control University of Stuttgart Stuttgart 70569 Germany

The paper focuses on the development of the navigation function approach for nonlinear systems with fast oscillating controls. This approach allows to solve the obstacle avoidance problem and generate reference trajectories on the state space with obstacles by using the gradient flow of a navigation function. In general, such gradient flow cannot be implemented for underactuated control systems, and an approximation of non-admissible velocities is needed for the control design. We present here an approximation result under low-order controllability assumptions. Our control design scheme is illustrated by an example of a nonholonomic system. © 2017

关键词： analytic design application of nonlinear analysis asymptotic stabilization control of constrained systems design Lyapunov methods

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Studying the natural gas market under demand uncertainty using a heterogeneous distributed computing environment

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Journal of Physics: Conference Series 2019年第7期1333卷

作者： V I Zorkalzev A V Edelev S M Perzhabinsky I A Sidorov A G Feoktistov Melentiev Energy Systems Institute Lermontov St. 130 Irkutsk Russia 664033 Matrosov Institute for System Dynamics and Control Theory SB RAS Lermontov St. 134 Irkutsk Russia 664033

In the paper, we propose a new model of the natural gas market simulation. It takes into account the random nature of the natural gas demand that depends, for example, on temperature fluctuations during the heating period. The natural gas supplier strategy is optimized with the reservation of the necessary amount of fuel to compensate for demand fluctuations. To implement simulation modeling, we developed a scalable application with the DISCOMP framework. We apply DISCOMP to develop and use scalable applications in a heterogeneous distributed computing environment. The application significantly increases the number of model runs and improves the simulation accuracy in comparison with the Mathcad computations on a personal computer.

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Subject-oriented computing environment for solving large-scale problems of energy security research

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Journal of Physics: Conference Series 2019年第5期1368卷

作者： I V Bychkov G A Oparin A G Feoktistov I A Sidorov S A Gorsky R O Kostromin A V Edelev Matrosov Institute for System Dynamics and Control Theory SB RAS Lermontov Street 134 Irkutsk Russia 664033 Melentiev Energy Systems Institute SB RA Lermontov Street 130 Irkutsk Russia 664033

We represent a new approach to the development and use of a subject-oriented heterogeneous distributed computing environment for solving large-scale problems of energy security research. Both the development of scalable applications (distributed applied software packages) and the computing resources integration are conducted using the Orlando Tools framework. It supports the collaborative application development based on the continuous integration of their software. Computation management tools in Orlando Tools are integrated with a multi-agent system. We propose special multi-agent tools for the heterogeneous resource allocation in the environment. These tools apply knowledge about the subject domain specifics of solved-problems and computing environment characteristics. The effectiveness of such management is highlighted by the results of solving practical problems of energy security research.

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A Novel Observer Approach for Self Sensing of Single-Coil Digital Valves

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IFAC-PapersOnLine 2017年第1期50卷 782-787页

作者： Braun T. Reuter J. Rudolph J. Institute of System Dynamics Konstanz University of Applied Sciences Konstanz 78462 Germany Chair of Systems Theory and Control Engineering Saarland University Campus A5 1 Saarbrücken 66123 Germany

Observer-based self sensing for digital (on–off) single-coil solenoid valves is investigated. Self sensing refers to the case where merely the driving signals used to energize the actuator (voltage and coil current) are available to obtain estimates of both the position and velocity. A novel observer approach for estimating the position and velocity from the driving signals is presented, where the dynamics of the mechanical subsystem can be neglected in the model. Both the effect of eddy currents and saturation effects are taken into account in the observer model. Practical experimental results are shown and the new method is compared with a full-order sliding mode observer. © 2017

关键词： Observer design Self sensing actuators Singular perturbation analysis

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