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Evaluation of the Index and Singular Points of Linear Differential-Algebraic Equations of Higher Order

Journal of Mathematical Sciences (United States) 2018年第6期231卷 827-845页

作者： Chistyakov, V.F. Chistyakova, E.V. Institute of the Dynamics of Systems and Control Theory Siberian Division of the Russian Academy of Sciences Irkutsk Russian Federation

We study linear systems of ordinary differential equations of higher order with an identically singular matrix at the higher derivative of the required vector-valued function in the domain of definition. We give definitions of the index and singular points for these systems, formulate the conditions of solvability, and deduce a formula for the general solution. The algorithms for finding the index and singular points are presented. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： ORDINARY differential equations LINEAR differential equations DOMAIN (Mathematics) DERIVATIVES (Mathematics) MATHEMATICAL singularities ALGEBRAIC equations

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Modeling of a RF Surgical Generator based on a Push-Pull Oscillator

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IFAC-PapersOnLine 2019年第15期52卷 382-387页

作者： Philip L. Neureuther Michael Ederer Peter Selig Matthias A. Müller Institute for System Dynamics University of Stuttgart Germany Erbe Elektromedizin GmbH Tübingen Germany Institute for Systems Theory and Automatic Control University of Stuttgart Germany Institute of Automatic Control Leibniz University Hanover Germany

To reduce manufacturing costs, a new simple radio frequency (RF) surgical generator based on a push-pull oscillator is developed for cutting tissue. In order to systematically design and test feedback controllers keeping the generator’s output voltage constant, we will present two different models of the considered RF generator. The first one is a nonlinear state space model derived using the generator’s equivalent circuit diagram and Kirchhoff’s laws and the second one is a Hammerstein model. The models are based on physical principles and are successfully validated on a generator prototype, ensuring a good match with the static and dynamic behavior of the considered RF generator. The obtained state space model is well suited to simulate the RF generator, while the Hammerstein model is appropriate to design controllers for the generator’s output voltage.

关键词： surgical generator push-pull oscillator equivalent circuit model state space model Hammerstein model

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Efficient structure-preserving support tensor train machine

arXiv

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arXiv 2020年

作者： Kour, Kirandeep Benner, Peter Dolgov, Sergey Stoll, Martin Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems MagdeburgD-39106 Germany Department of Mathematical Sciences University of Bath BathBA2 7AY United Kingdom Faculty of Mathematics Technische Universität Chemnitz ChemnitzD-09107 Germany

An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor classification methods. In the presence of small amounts of training data, kernel methods offer an attractive choice as they provide the possibility for a nonlinear decision boundary. We develop the Tensor Train Multi-way Multi-level Kernel (TT-MMK), which combines the simplicity of the Canonical Polyadic decomposition, the classification power of the Dual Structure-preserving Support Vector Machine, and the reliability of the Tensor Train (TT) approximation. We show by experiments that the TT-MMK method is usually more reliable computationally, less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification when benchmarked against other state-of-the-art techniques. Copyright © 2020, The Authors. All rights reserved.

关键词： Tensors

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Modelling energy systems of Vietnam with integration of renewable power sources 1

Modelling energy systems of Vietnam with integration of rene...

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1st International Workshop on Information, Computation, and control systems for Distributed Environments, ICCS-DE 2019

作者： Edelev, A.V. Karamov, D.N. Sidorov, I.A. Binh, D.V. Nam, N.H. Anh, N.H. Duy, P.V. Hanh, P.T. Melentiev Energy Systems Institute of Siberian Branch of SB RAS Lermontov St. 130 Irkutsk664033 Russia Matrosov Institute for System Dynamics and Control Theory of SB RAS Lermontov St. 134 Irkutsk664033 Russia Institute of Energy Science of VAST Block A9 Hoang Quoc Viet Street Cau Giay District Hanoi Viet Nam

The paper addresses the research of the large-scale penetration of renewable energy into the power system of Vietnam. The proposed approach presents the optimization of operational decisions in different power generation technologies as a Markov decision process. It uses a stochastic base model that optimizes a deterministic lookahead model. The first model applies the stochastic search to optimize the operation of power sources. The second model captures hourly variations of renewable energy over a year. The approach helps to find the optimal generation configuration under different market conditions. Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

关键词： Renewable energy resources

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Optimization of the composition of the structure of heat sources as applied to the problems of the development of heating systems

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IOP Conference Series: Earth and Environmental Science 2020年第1期408卷

作者： V A Stennikov O A Edeleva E S Fereferov Melentiev Energy Systems Institute of SB RAS Russia Matrosov Institute for System Dynamics and Control Theory of SB RAS Russia

The study outlines the concept of the structure of heat sources of developing heating systems and states the problem of searching through structures of heat sources of maximum redundancy for the optimal one. As one of the techniques of solving this problem, the authors propose to split the process of designing heating systems into multiple stages. Within the scope of the above-stated problem, the difficult part is the need to create an automated system to solve the entirety of problems arising at these stages and to reconcile them with each other. We provide a brief overview of the the available software package that we propose to integrate into the process of solving and we underline the complex nature of the interaction of individual software components between each other. The authors propose an approach in the form of the computational experiment setup that enables to consistently coordinate computational procedures with each other. The approach is based on the concept of the energy hub as its theoretical backbone, while in terms of the software implementation it is an instance of an automated information system.

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On an invariance principle for the solution space of the differential riccati equation

On an invariance principle for the solution space of the dif...

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89th Annual Meeting on the International Association of Applied Mathematics and Mechanics, GAMM 2018

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

The differential Riccati equation appears in different fields of applied mathematics like control theory and systems theory. For large-scale systems the numerical solution comes with a large amount of storage requirements. This motivates the use of Krylov subspace and projection based methods [1–3]. In the present paper we apply an invariance theorem for ODEs to the differential Riccati Equation. We show that the solution is contained in a Krylov like subspace and extend our results to certain time-varying cases. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

关键词： Riccati equations

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Constrained Gaussian process learning for model predictive control

arXiv

引用

arXiv 2019年

作者： Matschek, Janine Himmel, Andreas Sundmacher, Kai Findeisen, Rolf Laboratory for Systems Theory and Automatic Control Otto-von-Guericke University Magdeburg Germany Process Systems Engineering Otto-von-Guericke University Magdeburg Germany Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany

Many control tasks can be formulated as a tracking problem of a known or unknown reference signal. Examples are movement compensation in collaborative robotics, the synchronisation of oscillations for power systems or reference tracking of recipes in chemical process operation. Tracking performance as well as guaranteeing stability of the closed loop strongly depends on two factors: Firstly, it depends on whether the future desired tracking reference signal is known and, secondly, whether the system can track the reference at all. This paper shows how to use machine learning, i.e. Gaussian processes, to learn a reference from (noisy) data, while guaranteeing trackability of the modified desired reference predictions in the framework of model predictive control. Guarantees are provided by adjusting the hyperparameters via a constrained optimization. Two specific scenarios, i.e. asymptotically constant and periodical references, are discussed. Copyright © 2019, The Authors. All rights reserved.

关键词： Gaussian distribution

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Exact Optimization: Part I

arXiv

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arXiv 2019年

作者： Lin, Li-Gang Liang, Yew-Wen The Department of Mechanical Engineering National Central University Taoyuan32001 Taiwan The Department of Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39106 Germany The Institute of Electrical Control Engineering National Yang Ming Chiao Tung University Hsinchu30010 Taiwan

Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that relates CQE to convex quadratic function (CQF). More specifically, regarding the solvability of CQE, its necessary and sufficient condition as well as a unified parameterization of all the solutions has recently been analytically formulated. Moving forward, the understanding of CQE is utilized to describe the geometric structure of CQF, and the CQE-CQF relation. All these results are shown closely related to a basis in the optimization literature, namely quadratic programming (QP). For the first time from this viewpoint, the QPs subject to equality, inequality, equality-and-inequality, and extended constraints can be algebraically solved in derivative-free closed formulae, respectively. All the results are derived without knowing a feasible point, a priori and any time during the *** Codes Primary: 15A18, 52A41, 90C20, 90C25, and 90C46 Copyright © 2019, The Authors. All rights reserved.

关键词： Matrix algebra

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On extremum seeking controllers based on the lie bracket approximation in domains with obstacles

On extremum seeking controllers based on the lie bracket app...

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89th Annual Meeting on the International Association of Applied Mathematics and Mechanics, GAMM 2018

作者： Grushkovskaya, Victoria Zuyev, Alexander Ebenbauer, Christian Institute for Systems Theory and Automatic Control University of Stuttgart Germany Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Institute of Applied Mathematics & Mechanics National Academy of Sciences of Ukraine Ukraine

In this paper, we consider the problem of extremum seeking in the presence of obstacles. The analytical expression of the cost function as well as locations and shapes of the obstacles are assumed to be partially or completely unknown. We describe a broad family of control algorithms for a unicycle type system, which provides a solution of the above problem based on Lie bracket approximation ideas. The obtained controllers generalize some known results and allow to construct new control strategies. Furthermore, it is shown that gradient-free control algorithms can be used for excluding the attraction of trajectories to undesirable equilibriuma in obstacle avoidance problems. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

关键词： controllers

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Machine learning in a multi-agent system for distributed computing management 4

Machine learning in a multi-agent system for distributed com...

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4th International Conference on Information Technology and Nanotechnology - Session: Data Science, DS-ITNT 2018

作者： Bychkov, I.V. Feoktistov, A.G. Sidorov, I.A. Edelev, A.V. Gorsky, S.A. Kostromin, R.O. Matrosov Institute for System Dynamics and Control Theory SB RAS Lermontov St. 134 Irkutsk664033 Russia Melentiev Energy Systems Institute Lermontov St. 130 Irkutsk664033 Russia

We address the relevant problem of machine learning in a multi-agent system for distributed computing management. We propose a new approach to the agent learning in the system for managing job flows of scalable applications in a heterogeneous distributed computing environment, which includes high-performance computing clusters, as its main components. We manage parameter sweep applications that execute their jobs in a virtual machine environment. We use the specialized tools to implement such environment. In contrast to the known approaches, our approach is based on the integrated applying of methods for job classification and parameter adjustment of algorithms for functioning agents. Simulation modeling the environment allows eliciting the necessary knowledge for parameter adjustment. During the learning of agents, we use the expert knowledge of environment node administrators. An example of solving the complex practical problem that relates to studying energy development directions of Russia demonstrates advantages of the proposed approach. © 2018 CEUR-WS. All rights reserved.

关键词： Multi agent systems

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