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IEEE Multi-conference on Systems and Control

作者： Diego de S. Madeira Jurgen Adamy Control Methods and Robotics Lab Technische Universitat Darmstadt

ISBN: (纸本)9781509007561

This note deals with the static output feedback stabilization problem of linear time-invariant (LTI) systems, one of the most relevant open problems in the field of control theory. We present a new sufficient linear matrix inequality (LMI) condition to test stabilizability by static output feedback. The notion of passivity indices, as a measure of the level of passivity of a system, is employed. Unlike the methods currently available in the literature, our LMI condition is non iterative and does not rely on similarity transformations, allowing for a straightforward determination of a constant feedback gain that asymptotically stabilizes the closed-loop. We also provide numerical examples of our strategy in order to demonstrate its applicability in different scenarios.

关键词： Output feedback linear systems Nonlinear systems linear matrix inequalities Iterative methods Indexes

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Matrix GPBiCG algorithms for solving the general coupled matrix equations

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IET CONTROL theory AND applications 2015年第1期9卷 74-81页

作者： Hajarian, Masoud Shahid Beheshti Univ Fac Math Sci Dept Math Tehran 19839 Iran

linear matrix equations have important applications in control and system theory. In the study, we apply Kronecker product and vectorisation operator to extend the generalised product bi-conjugate gradient (GPBiCG) algorithms for solving the general coupled matrix equations Sigma(l)(j=1)(A)(i,1),jX1Bi,(1,j)+A(i),2,jX2Bi,2,j+...+A(i,l,j)X(i,l,j))=D(i)fori=1,2,...,l (including the (coupled) Sylvester, the second-order Sylvester and coupled Markovian jump Lyapunov matrix equations). We propose four effective matrix algorithms for finding solutions of the matrix equations. numerical examples and comparison with other well-known algorithms demonstrate the effectiveness of the proposed matrix algorithms.

关键词： conjugate gradient methods matrix algebra linear matrix equations Kronecker product vectorisation operator generalised product bi-conjugate gradient GPBiCG algorithm general coupled matrix equations system theory control theory generalised Sylvester matrix equation coupled Markovian jump Lyapunov matrix equation

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Research about the Special Type Matrix to Proof and Solve the Method of linear algebra 12

Research about the Special Type Matrix to Proof and Solve th...

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IEEE 12th International conference on Networking, Sensing and Control

作者： Li, Yan Lin Dai, Chien-Yun Natl Taiwan Normal Univ Dept Elect Engn Taipei Taiwan Natl Taiwan Normal Univ Dept Ind Educ Taipei Taiwan

ISBN: (纸本)9781479980697

"Data century has arrived! Having too many applications to discrete mathematics rather than use continuous mathematics, the method instead of using analog to digital methods. The vector and matrix has become the language which we must speak up." says the author of the professor named Gibert, S. linear algebra is a branch of mathematics that studies the object is a vector, a vector space (or linear space), and finite-dimensional linear transformation of linear equations. Vector space is an important topic in modern mathematics. linear algebra is widely used in abstract algebra and functional analysis;through analytic geometry, linear algebra to be specific representation. The theory of linear algebra has been generalized to operator theory. Due to the science of nonlinear models can be approximated by the linear models. linear algebra was widely used in the natural sciences, engineering, computer and social science. linear algebra originated in the two-dimensional and three-dimensional Cartesian coordinate system research.

关键词： Jordan canonical form minimal ploynomial quadratic curve positive definition and negative definition

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Revisiting the Nystrom Method for Improved Large-scale Machine Learning

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JOURNAL OF MACHINE LEARNING RESEARCH 2016年 17卷 1-65页

作者： Gittens, Alex Mahoney, Michael W. Univ Calif Berkeley Int Comp Sci Inst Berkeley CA 94720 USA Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA

We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results consist of an empirical evaluation of the performance quality and running time of sampling and projection methods on a diverse suite of SPSD matrices. Our results highlight complementary aspects of sampling versus projection methods;they characterize the effects of common data preprocessing steps on the performance of these algorithms;and they point to important differences between uniform sampling and nonuniform sampling methods based on leverage scores. In addition, our empirical results illustrate that existing theory is so weak that it does not provide even a qualitative guide to practice. Thus, we complement our empirical results with a suite of worst-case theoretical bounds for both random sampling and random projection methods. These bounds are qualitatively superior to existing bounds-e.g., improved additive-error bounds for spectral and Frobenius norm error and relative-error bounds for trace norm error-and they point to future directions to make these algorithms useful in even larger-scale machine learning applications.

关键词： Nystrom approximation low-rank approximation kernel methods randomized algorithms numerical linear algebra

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Neural-network-based adaptive leader-following consensus control for second-order non-linear multi-agent systems

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IET CONTROL theory AND applications 2015年第13期9卷 1927-1934页

作者： Wen, Guo-Xing Chen, C. L. Philip Liu, Yan-Jun Liu, Zhi Binzhou Univ Dept Math Binzhou 256600 Shandong Peoples R China Univ Macau Fac Sci & Technol Dept Comp & Informat Sci Macau Peoples R China UMacau Res Inst Zhuhai Guandong Peoples R China Liaoning Univ Technol Coll Sci Jinzhou 121001 Liaoning Peoples R China Guangdong Univ Technol Dept Automat Guangzhou 510006 Guangdong Peoples R China

In this study, a novel adaptive neural network (NN)-based leader-following consensus approach is proposed for a class of non-linear second-order multi-agent systems. For the existing NN consensus approaches, to obtain the desired approximation accuracy, the NN-based adaptive consensus algorithms require the number of NN nodes to must be large enough, and thus the online computation burden often are very heavy. However, the proposed adaptive consensus scheme can greatly reduce the online computation burden, because the adaptive adjusting parameters are designed in scalar form, which is the norm of the estimation of the optimal NN weight matrix. According to Lyapunov stability theory, the proposed approach can guarantee the leader-following consensus behaviour of non-linear second-order multi-agent systems to be obtained. Finally, a numerical simulation and a multi-manipulator simulation are carried out to further demonstrate the effectiveness of the proposed consensus approach.

关键词： multi-agent systems adaptive control neurocontrollers matrix algebra Lyapunov methods numerical analysis nonlinear control systems neural network adaptive leader following consensus control second order nonlinear multiagent systems leader following consensus approach NN based adaptive consensus algorithms NN nodes online computation optimal NN weight matrix Lyapunov stability theory numerical simulation multimanipulator simulation

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Alinea: An Advanced linear algebra Library for Massively Parallel Computations on Graphics Processing Units

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INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING applications 2015年第3期29卷 284-310页

作者： Magoules, Frederic Ahamed, Abal-Kassim Cheik Ecole Cent Paris Dept Math Dept Comp Sci F-92295 Chatenay Malabry France Ecole Cent Paris F-92295 Chatenay Malabry France

Direct and iterative methods are often used to solve linear systems in engineering. The matrices involved can be large, which leads to heavy computations on the central processing unit. A graphics processing unit can be used to accelerate these computations. In this paper, we propose a new library, named Alinea, for advanced linear algebra. This library is implemented in C++, CUDA and OpenCL. It includes several linear algebra operations and numerous algorithms for solving linear systems. For both central processing unit and graphic processing unit devices, there are different matrix storage formats, and real and complex arithmetics in single- and double-precision. The CUDA version includes a self-tuning of the grid, i.e. threading distribution, depending upon the hardware configuration and the size of the problems. numerical experiments and comparison with existing libraries illustrates the efficiency, accuracy and robustness of the proposed library.

关键词： Alinea linear algebra direct solvers iterative solvers parallel computing CPU GPU CUDA OpenCL auto-tuning energy efficiency

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Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

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AIP conference Proceedings 2017年第1期1907卷

作者： Yuri Grigor’ev Klaus Gürlebeck Dmitrii Legatiuk Theoretical Physics Department North-Eastern Federal University 58 Belinsky Str. Yakutsk 677000 Russia Academy of Sciences of the Republic of Sakha Yakutia 33 Lenin Av. Yakutsk 677007 Russia Chair of Applied Mathematics Bauhaus-Universität Weimar Coudraystr. 13B Weimar 99423 Germany Research Training Group 1462 Bauhaus-Universität Weimar Marienstr. 7A Weimar 99423 Germany

Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

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Learning HMMs with Nonparametric Emissions via Spectral Decompositions of Continuous Matrices 16

Learning HMMs with Nonparametric Emissions via Spectral Deco...

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Annual conference on Neural Information Processing Systems

作者： Kirthevasan Kandasamy Maruan Al-Shedivat Eric P. Xing Carnegie Mellon University Pittsburgh PA 15213

ISBN: (纸本)9781510838819

Recently, there has been a surge of interest in using spectral methods for estimating latent variable models. However, it is usually assumed that the distribution of the observations conditioned on the latent variables is either discrete or belongs to a parametric family. In this paper, we study the estimation of an m-state hidden Markov model (HMM) with only smoothness assumptions, such as Holderian conditions, on the emission densities. By leveraging some recent advances in continuous linear algebra and numerical analysis, we develop a computationally efficient spectral algorithm for learning nonparametric HMMs. Our technique is based on computing an SVD on nonparametric estimates of density functions by viewing them as continuous matrices. We derive sample complexity bounds via concentration results for nonparametric density estimation and novel perturbation theory results for continuous matrices. We implement our method using Chebyshev polynomial approximations. Our method is competitive with other baselines on synthetic and real problems and is also very computationally efficient.

关键词： spectral methods matrices sample complexity Hidden Markov models viewing perturbation theory Learning Emissions numerical Analysis CHEBYSHEV POLYNOMIALS

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Alinea: An Advanced linear algebra Library for Massively Parallel Computations on Graphics Processing Units

Alinea: An Advanced Linear Algebra Library for Massively Par...

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Exascale applications and Software conference (EASC)

作者： Magoules, Frederic Ahamed, Abal-Kassim Cheik Ecole Cent Paris Dept Math Dept Comp Sci F-92295 Chatenay Malabry France Ecole Cent Paris F-92295 Chatenay Malabry France

关键词： Alinea linear algebra direct solvers iterative solvers parallel computing CPU GPU CUDA OpenCL auto-tuning energy efficiency

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Direction-cosine-matrix-based attitude control subject to actuator saturation

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IET CONTROL theory AND applications 2015年第11期9卷 1653-1661页

作者： Forbes, James Richard Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA

Set-point attitude control of a rigid body explicitly preventing actuator saturation is considered. The attitude control approach developed does not employ any sort of direction-cosine-matrix (DCM) parameterisation, such as Euler angles or quaternions. Rather, the DCM is used directly within the feedback control algorithm. Together a proportional control term and an angular velocity control term make up the attitude controller. The angular velocity control is composed of a strictly positive real system subject to a special input non-linearity. The specific form of the proportional control and angular velocity control ensure control torques are below the saturation level of the on-board actuators. Two controller synthesis methods are considered. The first uses the linearised system, the solution to the linear quadratic regulator problem, and the Kalman-Yakubovich-Popov lemma to design the controller. The second employs a simple low-pass filter that is guaranteed to stabilise the closed-loop system;tuning the low-pass filter is also considered. numerical simulation results demonstrate effective closed-loop control in the presence of plant disturbances and sensor noise.

关键词： attitude control matrix algebra feedback angular velocity control control nonlinearities control system synthesis linearisation techniques linear quadratic control closed loop systems low-pass filters aerospace robotics direction-cosine-matrix-based attitude control actuator saturation set-point attitude control rigid body direction-cosine-matrix parameterisation DCM Euler angles quaternions feedback control algorithm angular velocity control term input nonlinearity proportional control on-board actuators controller synthesis methods linearised system linear quadratic regulator problem Kalman–Yakubovich–Popov lemma low-pass filter closed-loop system plant disturbances sensor noise

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