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International Carpathian Control conference (ICCC)

作者： Wojciech M. Kempa Department of Mathematics Applications and Methods for Artificial Intelligence Silesian University of Technology Gliwice Poland

ISBN: (数字)9798350350708

ISBN: (纸本)9798350350715

The problem of energy savings is today a key challenge in the process of designing service systems and their control mechanisms. On the one hand, the aim is to make maximum use of the technical and operational capabilities of the service station. On the other hand, however, it requires periodic technical inspections and maintenances, which causes its temporary immobilization and suspension of the job (customer, packet, call, etc.) service process. In the paper, we propose a queueing model of service process with finite accumulation buffer capacity in which a mechanism of energy saving is implemented based on single vacation policy. Namely, each time when the system empties the service station begins a vacation period of random duration in which the service process is blocked to save the energy. During the vacation period the service station can be maintained but, in some cases, it also can process secondary jobs then. The vacation period, however, may be shortened if the number of jobs accumulated in the buffer is close to its maximum capacity. Such an approach allows to achieve a balance between energy savings and ensuring appropriate quality of service (minimizing the risk of job losses due to buffer overflow). The explicit-form analytic representation for the queue-size distribution in the considered system will be found using the approach based on the idea of embedded Markov chain and linear algebra. numerical examples illustrating the impact on key system input parameters on the queue-size distribution will be attached, as well.

关键词： Laplace equations Energy conservation Process control Quality of service Matrices numerical models Servers

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System Parameter and State Estimator over Unknown linear Systems

System Parameter and State Estimator over Unknown Linear Sys...

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American Control conference (ACC)

作者： Ding, Xuda He, Jianping Chen, Cailian Guan, Xinping Shanghai Jiao Tong Univ Minist Educ China Key Lab Syst Control & Informat Proc Dept Automat Shanghai 200240 Peoples R China Shanghai Engn Res Ctr Intelligent Control & Manag Shanghai 200240 Peoples R China

ISBN: (纸本)9781665441971

System model parameter and state estimations are classical problems for control theory. Most of the existing methods have promising results under the condition that the prior knowledge of the system model is known (system structure is given). However, in practical applications, the accuracy of prior knowledge degenerates over time, which causes identification failure. Besides, the estimation error bounds are needed for most of the low-cost model-based controller design. In this paper, we aim to design a stable parameter and state estimator over the unknown linear system (i.e., without prior knowledge), via a suitable feedback gain and iterative adjustment procedure and determine the error bounds. The insights of the proposed design lie in: i) the operation data can reflect the internal parameters of the model and provide a source for preliminary estimation;ii) the error bounds of estimated parameters and states can be determined based on mathematical analysis of the regression procedure. Specifically, the support vector regression (SVR) is used to estimate system parameters, and the feedback gain is designed to guarantee bounded-input, bounded-output (BIBO) stability. Then, the error bounds are given, and an adaptive adjustment procedure is adapted to increase the estimation accuracy. Finally, numerical simulations demonstrate the relative estimation error of the proposed estimator is less than 3.15%.

关键词： linear systems Support vector machines Estimation error Mathematical analysis Observers numerical simulation Stability analysis

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Solving linear Systems on a GPU with Hierarchically Off-Diagonal Low-Rank Approximations

Solving Linear Systems on a GPU with Hierarchically Off-Diag...

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Supercomputing conference

作者： Chao Chen Per-Gunnar Martinsson Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin United States Department of Mathematics Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin United States

ISBN: (纸本)9781665454452

We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the factorization of many large sparse matrices. The coefficient matrices are often data-sparse in the sense that their off-diagonal blocks have low numerical ranks; specifically, we focus on “hierarchically off-diagonal low-rank (HODLR)” matrices. We introduce algorithms for factorizing HODLR matrices and for applying the factorizations on a GPU. The algorithms leverage the efficiency of batched dense linear algebra, and they scale nearly linearly with the matrix size when the numerical ranks are fixed. The accuracy of the HODLR-matrix approximation is a tunable parameter, so we can construct high-accuracy fast direct solvers or low-accuracy robust preconditioners. numerical results show that we can solve problems with several millions of unknowns in a couple of seconds on a single GPU.

关键词： linear systems High performance computing Integral equations Graphics processing units Machine learning Approximation algorithms Matrices

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Advances in System Identification: theory and applications 60

Advances in System Identification: Theory and Applications

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60th IEEE conference on Decision and Control (CDC)

作者： Gueho, Damien Singla, Puneet Majji, Manoranjan Juang, Jer-Nan Penn State Univ Dept Aerosp Engn University Pk PA 16802 USA Texas A&M Univ Dept Aerosp Engn College Stn TX 77840 USA Texas A&M Univ College Stn TX 77840 USA

ISBN: (纸本)9781665436595

This paper describes the main features and the most recent developments of system identification in the sense of data-driven modeling of dynamical systems. A brief summary of discrete time-invariant system identification techniques is provided, from the modern work of Gilbert, Kalman and Ho and the introduction of state-space realization, to the most recent developments of the identification of discrete time-varying and nonlinear systems. Important concepts of state-space realization, controllability and observability for linear systems are introduced along with more advanced methods to identify nonlinear dynamics. numerical examples of varying complexity are considered to demonstrate the capability of the different approaches presented in this paper.

关键词： Invariance

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Optimizing Tensor Computations: From applications to Compilation and Runtime Techniques 23

Optimizing Tensor Computations: From Applications to Compila...

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2023 ACM/SIGMOD International conference on Management of Data, SIGMOD 2023

作者： Boehm, Matthias Interlandi, Matteo Jermaine, Chris TU Berlin Berlin Germany Mircosoft GSL Los AngelesCA United States Rice University HoustonTX United States

ISBN: (纸本)9781450395076

Machine learning (ML) training and scoring fundamentally relies on linear algebra programs and more general tensor computations. Most ML systems utilize distributed parameter servers and similar distribution strategies for mini-batch stochastic gradient descent training. However, many more tasks in the data science and engineering lifecycle can benefit from efficient tensor computations. Examples include primitives for data cleaning, data and model debugging, data augmentation, query processing, numerical simulations, as well as a wide variety of training and scoring algorithms. In this survey tutorial, we first make a case for the importance of optimizing more general tensor computations, and then provide an in-depth survey of existing applications, optimizing compilation techniques, and underlying runtime strategies. Interestingly, there are close connections to data-intensive applications, query rewriting and optimization, as well as query processing and physical design. Our goal for the tutorial is to structure existing work, create common terminology, and identify open research challenges. © 2023 ACM.

关键词： Machine learning

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An optimal control problem by a first-order hyperbolic system with delay and integral control constraints

An optimal control problem by a first-order hyperbolic syste...

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2020 Dynamic Systems and Computer Science: theory and applications, DYSC 2020

作者： Poplevko, V.P. Arguchintsev, A.V. Department of Computational Mathematics and Optimization Irkutsk State University 1 K. Marks St. Irkutsk664003 Russia

A non-classic optimality condition and numerical algorithm for smooth boundary control in semi-linear first-order hyperbolic system with delay are presented. An additional integral control constraint is considered. The suggested approach is based on special variations of admissible continuously differentiable controls. These variations lead to a necessary optimality condition which is a base for a numerical method. An illustrative example demonstrates the effectiveness of the proposed approach. © Published under licence by IOP Publishing Ltd.

关键词： numerical methods

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Subgradient Smoothing Method for Nonsmooth Nonconvex Optimization 5th

Subgradient Smoothing Method for Nonsmooth Nonconvex Optimiz...

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5th International conference on numerical Analysis and Optimization: theory, methods, applications and Technology Transfer, NAOV 2020

作者： Bagirov, A.M. Sultanova, N. Taheri, S. Ozturk, G. School of Engineering Information Technology and Physical Sciences Federation University Australia Ballarat Australia School of Science RMIT University Melbourne Australia Department of Industrial Engineering Eskisehir Technical University Eskisehir Turkey

ISBN: (纸本)9783030720391

In this chapter an unconstrained nonsmooth nonconvex optimization problem is considered and a method for solving this problem is developed. In this method the subproblem for finding search directions is reduced to the unconstrained minimization of a smooth function. This is achieved by using subgradients computed in some neighborhood of a current iteration point and by formulating the search direction finding problem to the minimization of the convex piecewise linear function over the unit ball. The hyperbolic smoothing technique is applied to approximate the minimization problem by a sequence of smooth problems. The convergence of the proposed method is studied and its performance is evaluated using a set of nonsmooth optimization academic test problems. In addition, the method is implemented in GAMS and numerical results using different solvers from GAMS are reported. The proposed method is compared with a number of nonsmooth optimization methods. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Piecewise linear techniques

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The algebra of splines: duality, group actions and homology

arXiv

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arXiv 2023年

作者： Lanini, Martina Schenck, Hal Tymoczko, Julianna Dipartimento di Matematica Universita di Roma Tor Vergata Italy Department of Mathematics Auburn University United States Department of Mathematics Smith College United States

This survey gives an overview of three central algebraic themes related to the study of splines: duality, group actions, and homology. Splines are piecewise polynomial functions of a prescribed order of smoothness on some subdivided domain D ⊆ Rk, and appear in applications ranging from approximation theory to geometric modeling to numerical analysis. Alternatively, splines can be interpreted as a collection of polynomials labeling the vertices of a (combinatorial) graph, with adjacent vertex-labels differing by a power of an affine linear form attached to the edge. In most cases of interest, the subdivided domain is essentially dual to the combinatorial graph, and these two characterizations of splines coincide. Properties of splines depend on combinatorics, topology, geometry, and symmetry of a simplicial or polyhedral subdivision Δ of a region D ⊆ Rk, and are often quite subtle. We describe how duality, group actions, and homology - techniques which play a central role in many areas of both pure and applied mathematics - can be used to illuminate different questions about splines. Our target audience is nonspecialists: we provide a concrete introduction to these methods, and illustrate them with many examples in the context of splines. We also provide a tutorial on computational aspects: all of the objects appearing in this note may be studied using open source computer algebra *** Codes Primary 41A15, Secondary 13D40, 14M25, 55N30 Copyright © 2023, The Authors. All rights reserved.

关键词： Open source software

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Computing Function of Large Matrices by a Preconditioned Rational Krylov Method

Computing Function of Large Matrices by a Preconditioned Rat...

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European conference on numerical Mathematics and Advanced applications, ENUMATH 2019

作者： Bertaccini, Daniele Durastante, Fabio Università di Roma "Tor Vergata" Dipartimento di Matematica viale della Ricerca Scientifica 1 Roma Italy Roma Italy Napoli Italy

ISBN: (纸本)9783030558734

Rational Krylov methods are a powerful alternative for computing the product of a function of a large matrix times a given vector. However, the creation of the underlying rational subspaces requires solving sequences of large linear systems, a delicate task that can require intensive computational resources and should be monitored to avoid the creation of subspace different to those required whenever, e.g., the underlying matrices are ill-conditioned. We propose the use of robust preconditioned iterative techniques to speedup the underlying process. We also discuss briefly how the inexact solution of these linear systems can affect the computed subspace. A preliminary test approximating a fractional power of the Laplacian matrix is included. © 2021, Springer Nature Switzerland AG.

关键词： Matrix algebra

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THERMOACOUSTIC STABILITY ANALYSIS OF A FULL-ANNULAR LEAN COMBUSTOR FOR HEAVY-DUTY applications

THERMOACOUSTIC STABILITY ANALYSIS OF A FULL-ANNULAR LEAN COM...

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ASME Turbomachinery Technical conference and Exposition (Turbo Expo) - Sustainable Energy - Accelerating the Transition by Advancing Turbine Technology

作者： Pampaloni, Daniele Andreini, Antonio Marini, Alessandro Riccio, Giovanni Ceccherini, Gianni Univ Florence Dept Ind Engn Via S Marta 3 I-50139 Florence Italy Baker Hughes Via F Matteucci 2 I-50139 Florence Italy

ISBN: (纸本)9780791884942

Thermoacoustic characterization of gas turbine combustion systems is of primary importance for successful development of gas turbine technology, to meet the stringent targets on pollutant emissions. In this context, it becomes more and more necessary to develop reliable tools to be used in the industrial design process. The dynamics of a lean-premixed full-annular combustor for heavy-duty applications has been numerically studied in this work. The well-established CFD-SI method has been used to investigate the flame response varying operational parameters such as the flame temperature (global equivalence ratio) and the fuel split between premixed and pilot fuel injections: such a wide range experimental characterization represents an opportunity to validate the employed numerical methods and to give a deeper insight into the flame dynamics. URANS simulations have been performed, due to their affordable computational costs from the industrial perspective, after validating their accuracy through the comparison against LES results. Furthermore, an approach where the pilot and the premixed flame responses are analyzed separately is proposed, exploiting the independence of their evolution. The calculated FTFs have been implemented in a 3D FEM model of the chamber, in order to perform linear stability analysis and to validate the numerical approach. A boundary condition for rotational periodicity based on Bloch-Wave theory has been implemented into the Helmholtz solver and validated against fullannular chamber simulations, allowing a significant reduction in computational time. The reliability of the numerical procedure has been assessed through the comparison against full-annular experimental results.

关键词： Stability Combustion chambers Flames Engineering simulation Gas turbines Simulation Fuels Dynamics (Mechanics) Reliability Temperature Industrial design Waves Finite element methods Combustion systems Computational fluid dynamics numerical analysis Boundary-value problems Finite element model Pollution Emissions Experimental characterization

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