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11th International conference and Exposition on Electrical And Power Engineering, EPE 2020

作者： Galatanu, Catalin Daniel Gherasim, Iulian Gheorghe Asachi Technical University Department of Building Services Engineering Iasi Romania

ISBN: (纸本)9781728181264

linear lamps (fluorescent or LED) represent a suitable option for specific applications. For near field simulations, such as coves or luminaires, the usual mathematical representation is not sufficient. A photometric file (*** ***) is only valid for normal interior lighting, not for near field, and the traditional theory doesn't have any solving approach. The present paper proposes a method to solve these limitations, and a numerical model is developed and presented. The validation method is based on experimental results, for a test problem. © 2020 IEEE.

关键词： numerical methods

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Sufficient Condition for the Existence of a Limit Cycle in Integrated Relay Output Feedback Systems

Sufficient Condition for the Existence of a Limit Cycle in I...

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Control Technology and applications (CCTA),

作者： Yongeun Yoon Woojin Choi Agency for Defence Development Daejeon KOR South Korea

ISBN: (纸本)9781665436441

An integrated relay output feedback (IROF) system is a piecewise linear system representing many electric and/or mechanical systems. Like other piecewise linear systems IROF inherently has limit-cycle oscillation(LCO), which plays a critical role in the performance of the system, entailing the necessity of reliable analysis on the LCO. However, due to the nature of the solution trajectory of LCO, we cannot safely apply existing methods on the analysis of LCO such as describing function, Floquet theory, or piecewise linear system analysis. This research provides a new theoretical approach with which to establish the sufficient condition of an LCO in the IROF system accompanying the analysis on its stability and main parameters. We start from confirming that the switching time between each switching plane is finite. Then, by the introduction of a discrete-time nonlinear system representing the Poincaré map and the linear phase can we establish the sufficient condition for the existence of an LCO and its stability. Finally, we demonstrate the effectiveness and efficiency of the main results with a simple numerical example.

关键词： linear systems Sufficient conditions Liquid crystal on silicon Limit-cycles Switches Stability analysis Trajectory

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Faster randomized infeasible interior point methods for tall/wide linear programs 34

Faster randomized infeasible interior point methods for tall...

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34th conference on Neural Information Processing Systems, NeurIPS 2020

作者： Chowdhury, Agniva London, Palma Avron, Haim Drineas, Petros Department of Statistics Purdue University West LafayetteIN United States ORIE Department Cornell University IthacaNY United States School of Mathematical Sciences Tel Aviv University Tel Aviv Israel Department of Computer Science Purdue University West LafayetteIN United States

linear programming (LP) is used in many machine learning applications, such as l1-regularized SVMs, basis pursuit, nonnegative matrix factorization, etc. Interior Point methods (IPMs) are one of the most popular methods to solve LPs both in theory and in practice. Their underlying complexity is dominated by the cost of solving a system of linear equations at each iteration. In this paper, we consider infeasible IPMs for the special case where the number of variables is much larger than the number of constraints (i.e., wide), or vice-versa (i.e., tall) by taking the dual. Using tools from Randomized linear algebra, we present a preconditioning technique that, when combined with the Conjugate Gradient iterative solver, provably guarantees that infeasible IPM algorithms (suitably modified to account for the error incurred by the approximate solver), converge to a feasible, approximately optimal solution, without increasing their iteration complexity. Our empirical evaluations verify our theoretical results on both real and synthetic data. © 2020 Neural information processing systems foundation. All rights reserved.

关键词： linear programming

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Max Plus algebra, Optimization and Game theory

Max Plus Algebra, Optimization and Game Theory

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International conference on Mathematical Analysis and applications in Modeling, ICMAAM 2018

作者： Dubey, Dipti Neogy, S.K. Sinha, Sagnik Indian Statistical Institute 7 S.J.S. Sansanwal Marg New Delhi110016 India Jadavpur University Kolkata India

ISBN: (纸本)9789811504211

Max-plus algebra has been applied to several fields like matrix algebra, cryptography, transportation, manufacturing, information technology and study of discrete event systems like subway traffic networks, parallel processing systems, telecommunication networks for many years. In this paper, we discuss various optimization problem using methods based on max-plus algebra, which has maximization and addition as its basic arithmetic operations. We present some sub-classes of mathematical optimization problems like linear programming, convex quadratic programming problem, fractional programming problem, bimatrix game problem and some classes of stochastic game problem in max algebraic framework and discuss various connections between max-plus algebra and optimization. © 2020, Springer Nature Singapore Pte Ltd.

关键词： linear programming

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Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection

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numerical linear algebra WITH applications 2021年第4期28卷 e2367-e2367页

作者： De Sterck, Hans Falgout, Robert D. Friedhoff, Stephanie Krzysik, Oliver A. MacLachlan, Scott P. Univ Waterloo Dept Appl Math Waterloo ON Canada Lawrence Livermore Natl Lab Ctr Appl Sci Comp Livermore CA 94550 USA Berg Univ Wuppertal Dept Math Wuppertal Germany Monash Univ Sch Math Clayton Vic Australia Mem Univ Newfoundland Dept Math & Stat St John NF Canada

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent partial differential equations (PDEs) in modern high-performance computing environments. While these techniques have been very successful for parabolic equations, it has often been observed that their performance suffers dramatically when applied to advection-dominated problems or purely hyperbolic PDEs using standard rediscretization approaches on coarse grids. In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically nonscalable or even divergent behavior of these solvers for this problem. To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory. One of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves. Our approach is tested for schemes of various orders using explicit or implicit Runge-Kutta methods combined with upwind-finite-difference spatial discretizations. In all cases, we obtain scalable convergence in just a handful of iterations, with parallel tests also showing significant speed-ups over sequential time-stepping.

关键词： high‐ order hyperbolic MGRIT multigrid parallel‐ in‐ time Parareal

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Internally positive representations and stability analysis of linear differential systems with multiple time-varying delays

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IET CONTROL theory AND applications 2019年第7期13卷 920-927页

作者： De Iuliis, Vittorio D'Innocenzo, Alessandro Germani, Alfredo Manes, Costanzo Univ Aquila Dipartimento Ingn & Sci Informaz & Mat Via Vetoio I-67100 Coppito AQ Italy

This work introduces the internally positive representation of linear time-varying delay differential systems, in the general case of multiple time-varying delays. The technique, previously established for the delay-free case and recently extended to various classes of linear delay systems, aims at building a positive representation of systems whose dynamics is, in general, not definite in sign, in order to export results that only hold for positive systems to arbitrary ones. In the special case of constant matrices, this leads to a simple and easy to check condition for the delay-independent stability of differential systems with multiple time-varying delays. The condition is shown to be less conservative than some well-known conditions available in the literature. numerical examples are proposed to validate the theoretical results.

关键词： delays stability linear systems delay systems matrix algebra time-varying systems Lyapunov methods delay-differential systems systems whose dynamics positive systems delay-independent stability multiple time-varying delays internally positive representation linear differential systems linear time-varying delay differential systems delay-free case linear delay systems

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algebraic proof methods for identities of matrices and operators: Improvements of Hartwig's triple reverse order law

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APPLIED MATHEMATICS AND COMPUTATION 2021年 409卷 126357-126357页

作者： Cvetkovic-Ilic, Dragana S. Hofstadler, Clemens Poor, Jamal Hossein Milosevic, Jovana Raab, Clemens G. Regensburger, Georg Univ Nis Dept Math Fac Sci & Math Nish Serbia Johannes Kepler Univ Linz Inst Algebra Linz Austria

When improving results about generalized inverses, the aim often is to do this in the most general setting possible by eliminating superfluous assumptions and by simplifying some of the conditions in statements. In this paper, we use Hartwig's well-known triple reverse order law as an example for showing how this can be done using a recent framework for algebraic proofs and the software package OperatorGB. Our improvements of Hartwig's result are proven in rings with involution and we discuss computer-assisted proofs that show these results in other settings based on the framework and a single computation with noncommutative polynomials. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Matrices and linear operators algebraic operator identities Generalized inverses Reverse order law Automated proofs Noncommutative polynomials Quiver representations

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Accelerating the Advanced-Step NMPC by a Lifted Implicit Runge-Kutta Integrator for Fast Embedded applications 39

Accelerating the Advanced-Step NMPC by a Lifted Implicit Run...

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39th Chinese Control conference (CCC)

作者： Zhu, Zhu Jiang, Canghua Jin, Cheng Guo, Zhiqiang Xu, Zongqi Hefei Univ Technol Sch Elect Engn & Automat Hefei Peoples R China Zhongxing Telecommun Equipment ZTE Corp Nanjing 210012 Peoples R China China Railway Signal & Commun Res & Design Inst G Beijing 100073 Peoples R China

ISBN: (纸本)9789881563903

In order to reduce computational delay, advanced-step nonlinear model predictive control (asNMPC) divides the on-line computation into two steps. In the first step, an optimal control problem with predicted initial state is solved. Then, the computed control action is corrected by sensitivity update in the second step once the measurement of state is available. Since sensitivity update is valid only for small perturbation, the steps for state prediction cannot be too many, and the time constraint for the computation of optimal control is still stringent. For fast embedded applications, this paper proposes to incorporate a lifted implicit Runge-Kutta (IRK) integrator in the scheme of asNMPC. The derived nonlinear program (NLP) is thus small and dense, and can be solved without resorting to sparse linear algebra solver. Furthermore, this integrator requires fewer Newton iterations, and possesses similar convergence property as the simultaneous collocation integrator originally used. Based on it, variational sensitivity propagation is applied for gradient computation, which is decoupled from the integration of nominal equation, and thus has improved efficiency. This algorithm is implemented based on Ipopt with sIPOPT library. Warm start for primal and dual variables and the Hessian of the Lagrangian is also implemented. numerical simulations on the control of a Delta robot demonstrate that the lifted IRK integrator can improve the computational efficiency of asNMPC considerably.

关键词： NMPC Differential-algebraic Equation Implicit Runge-Kutta Method Sensitivity Delta Robot

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Advances in System Identification: theory and applications

Advances in System Identification: Theory and Applications

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IEEE conference on Decision and Control

作者： Damien Guého Puneet Singla Manoranjan Majji Jer-Nan Juang The Pennsylvania State University PA Texas A&M University College Station TX Texas AM University College Station TX

ISBN: (纸本)9781665436601

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： linear systems Heuristic algorithms Robustness Nonlinear dynamical systems System identification Trajectory Kalman filters

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Optimal Restoration of Multiple Signals in Quaternion algebra

Optimal Restoration of Multiple Signals in Quaternion Algebr...

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conference on Mobile Multimedia/Image Processing, Security, and applications

作者： Grigoryan, Artyom M. Agaian, Sos S. Univ Texas San Antonio San Antonio TX 78249 USA CUNY CSI New York NY 10021 USA

ISBN: (纸本)9781510635760;9781510635753

This paper offers a new multiple signal restoration tool to solve the inverse problem, when signals are convoluted with a multiple impulse response and then degraded by an additive noise signal with multiple components. Inverse problems arise practically in all areas of science and engineering and refers to as methods of estimating data/parameters, in our case of multiple signals that cannot directly be observed. The presented tool is based on the mapping multiple signals into the quaternion domain, and then solving the inverse problem. Due to the non-commutativity of quaternion arithmetic, it is difficult to find the optimal filter in the frequency domain for degraded quaternion signals. As an alternative, we introduce an optimal filter by using special 4 x4 matrices on the discrete Fourier transforms of signal components, at each frequency-point. The optimality of the solution is with respect to the mean-square-root error, as in the classical theory of the signal restoration by the Wiener filter. The Illustrative example of optimal filtration of multiple degraded signals in the quaternion domain is given. The computer simulations validate the effectiveness of the proposed method.

关键词： Inverse problem of optimal filtration Wiener filter signal restoration quaternion linear convolution quaternion discrete Fourier transform

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