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Motion planning problem with obstacle avoidance for step-2 bracket-generating systems

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PAMM 2018年第1期17卷

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

This paper considers the obstacle avoidance problem for control-linear systems satisfying the Hörmander condition with the first-order Lie brackets. To solve the problem under consideration, we use a family of oscillating periodic control functions with state-dependent coefficients. The proposed approach is shown to be applicable for different shapes of obstacles and various potential functions generating collision-free paths. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Low-rank computation of posterior covariance matrices in Bayesian inverse problems

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arXiv 2017年

作者： Benner, Peter Qiu, Yue Stoll, Martin Computational Methods in Systems and Control Theory Group Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany Numerical Linear Algebra for Dynamical Systems Group Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

We consider the problem of estimating the uncertainty in statistical inverse problems using Bayesian inference. When the probability density of the noise and the prior are Gaussian, the solution of such a statistical inverse problem is also Gaussian. Therefore, the underlying solution is characterized by the mean and covariance matrix of the posterior probability density. However, the covariance matrix of the posterior probability density is full and large. Hence, the computation of such a matrix is impossible for large dimensional parameter spaces. It is shown that for many ill-posed problems, the Hessian matrix of the data misfit part has low numerical rank and it is therefore possible to perform a low-rank approach to approximate the posterior covariance matrix. For such a low-rank approximation, one needs to solve a forward partial differential equation (PDE) and the adjoint PDE in both space and time. This in turn gives O(nxnt) complexity for both, computation and storage, where nx is the dimension of the spatial domain and nt is the dimension of the time domain. Such computations and storage demand are infeasible for large problems. To overcome this obstacle, we develop a new approach that utilizes a recently developed low-rank in time algorithm together with the low-rank Hessian method. We reduce both the computational complexity and storage requirement from O(nxnt) to O(nx + nt). We use numerical experiments to illustrate the advantages of our approach. Copyright © 2017, The Authors. All rights reserved.

关键词： Constrained optimization

Universal spectra of random Lindblad operators

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arXiv 2018年

作者： Denisov, Sergey Laptyeva, Tetyana Tarnowski, Wojciech Chruściński, Dariusz Życzkowski, Karol Department of Computer Science Oslo Metropolitan University OsloN-0130 Norway Department of Control Theory and Systems Dynamics Lobachevsky University Gagarina Av. 23 Nizhny Novgorod603950 Russia Marian Smoluchowski Institute of Physics Uniwersytet Jagielló nski Krakow Poland Institute of Physics Faculty of Physics Astronomy and Informatics Nicolaus Copernicus University Grudziadzka 5/7 Torun87–100 Poland Centrum Fizyki Teoretycznej PAN Warszawa Poland

To understand typical dynamics of an open quantum system in continuous time, we introduce an ensemble of random Lindblad operators, which generate Markovian completely positive evolution in the space of density matrices. Spectral properties of these operators, including the shape of the spectrum in the complex plane, are evaluated by using methods of free probabilities and explained with non-Hermitian random matrix models. We also demonstrate universality of the spectral features. The notion of ensemble of random generators of Markovian qauntum evolution constitutes a step towards categorization of dissipative quantum chaos. Copyright © 2018, The Authors. All rights reserved.

关键词： Continuous time systems

A novel tube-based output feedback MPC for constrained linear systems

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A novel tube-based output feedback MPC for constrained linea...

American control Conference

作者： Sankaranarayanan Subramanian Sergio Lucia Sebastian Engell Process Dynamics and Operations Group TU Dortmund Germany Otto-von-Guericke-University Magdeburg Laboratory for Systems Theory and Automatic Control Institute of Automation Engineering Germany

ISBN: (纸本)9781509045839

Model Predictive control (MPC) is an advanced strategy for the control of multi-variable and constrained dynamical systems. Tube-based MPC is a robust control technique that handles uncertainties present in the model. Since full state information is seldom available in practical systems, the estimation error must also be taken into account in addition to model uncertainties to achieve closed-loop stability and constraint satisfaction despite estimation and model errors. In this paper, we propose a novel strategy for the design of a tube-based output feedback MPC which is independent of the estimation method employed. We formulate a control policy by choosing a candidate estimate that is consistent with the reachable sets of the system under control. The proposed method can be combined with any estimation scheme as long as the assumed error bounds are satisfied. We show that the proposed method is recursively feasible, robustly exponentially stable, and performs better than other available strategies.

关键词： Maximum Allowable Concentration Linear system control strategy Output feedback constraint satisfaction problems model error control technology model uncertainty Statistical analysis

On a class of generating vector fields for the extremum seeking problem: Lie bracket approximation and stability properties

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arXiv 2017年

作者： Grushkovskaya, Victoria Zuyev, Alexander Ebenbauer, Christian Institute for Systems Theory and Automatic Control University of Stuttgart Stuttgart70569 Germany Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39106 Germany Institute of Applied Mathematics and Mechanics National Academy of Sciences of Ukraine Sloviansk84100 Ukraine

In this paper, we describe a broad class of control functions for extremum seeking problems. We show that it unifies and generalizes existing extremum seeking strategies which are based on Lie bracket approximations, and allows to design new controls with favorable properties in extremum seeking and vibrational stabilization tasks. The second result of this paper is a novel approach for studying the asymptotic behavior of extremum seeking systems. It provides a constructive procedure for defining frequencies of control functions to ensure the practical asymptotic and exponential stability. In contrast to many known results, we also prove asymptotic and exponential stability in the sense of Lyapunov for the proposed class of extremum seeking systems under appropriate assumptions on the vector fields. Copyright © 2017, The Authors. All rights reserved.

关键词： Asymptotic stability

Position Observation for Proportional Solenoid Valves by Signal Injection

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IFAC-PapersOnLine 2016年第21期49卷 74-79页

作者： Braun, Tristan Reuter, Johannes Rudolph, Joachim Institute of System Dynamics Konstanz University of Applied Sciences Konstanz78462 Germany Chair of Systems Theory and Control Engineering Saarland University Campus A5 1 Saarbrücken66123 Germany

The method of signal injection is investigated for position estimation of proportional solenoid valves. A simple observer is proposed to estimate a position-dependent parameter, i.e. the eddy current resistance, from which the position is calculated analytically. Therefore, the relationship of position and impedance in the case of sinusoidal excitation is accurately described by consideration of classical electrodynamics. The observer approach is compared with a standard identification method, and evaluated by practical experiments on an off-the-shelf proportional solenoid valve. © 2016

关键词： Solenoid valves Electromagnets Hydraulic actuators Magnetic actuators Magnetic fields Parameter estimation Solenoids Classical electrodynamics Electromagnetic devices Identification method Observers Position dependents Position estimation Proportional solenoid valves Sinusoidal excitations

An inexact Newton-Krylov method for stochastic eigenvalue problems

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arXiv 2017年

作者： Benner, Peter Onwunta, Akwum Stoll, Martin Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstrasse 1 Magdeburg39106 Germany Numerical Linear Algebra for Dynamical Systems Group Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstrasse 1 Magdeburg39106 Germany Technische Universität Chemnitz Faculty of Mathematics Professorship Scientific Computing Chemnitz09107 Germany

This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product structure when discretized with the stochastic Galerkin method. Here, we exploit this inherent tensor product structure to develop a globalized low-rank inexact Newton method with which we tackle the stochastic eigenproblem. We illustrate the effectiveness of our solver with numerical experiments. Copyright © 2017, The Authors. All rights reserved.

关键词： Galerkin methods

Improving the Performance of Numerical Algorithms for the Bethe-Salpeter Eigenvalue Problem

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PAMM 2018年第1期18卷

作者： Peter Benner Andreas Marek Carolin Penke Max Planck Institute for Dynamics of Complex Technical Systems Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg Max Planck Computing and Data Facility Gießenbachstraße 2 85748 Garching

The Bethe-Salpeter eigenvalue problem arises in the computation of the electronic structure of many-body physical systems. The resulting matrix is complex, admits a certain block structure and can become extremely large. This raises the need for structure-preserving algorithms running in parallel on high performance compute clusters. In this paper we examine how a recently proposed direct method given in the BSEPACK library can be improved using eigenvalue solvers from the ELPA library. For large matrices a runtime reduction of up to 80% is achieved.

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Linear Low-Rank Parameter-Dependent Fluid-Structure Interaction Discretization in 2D

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PAMM 2018年第1期18卷

作者： Roman Weinhandl Peter Benner Thomas Richter Max Planck Institute for Dynamics of Complex Technical Systems Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg Otto von Guericke University Magdeburg Faculty of Mathematics Universitätsplatz 2 39106 Magdeburg

Fluid-structure interaction problems involve material parameters such as the shear modulus of the solid and the dynamic fluid viscosity. In order to examine the behaviors of various solids and adapt the problems to different fluid configurations there is a need to vary such material parameters flexibly. This can be done by a parameter-dependent fluid-structure interaction discretization which yields a system matrix that has block diagonal structure. As also discussed in [2], the resulting equation is equivalent to a matrix equation which allows for a low-rank approach where the iterate is represented by a tensor. A low-rank GMRES variant similar to what was discussed in [1] can then be applied to such parameter-dependent systems.

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