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18th IEEE conference on Industrial Electronics and applications, ICIEA 2023

作者： Feng, Shaofan Liu, Lei North China University of Technology Beijing China

ISBN: (纸本)9798350312201

The problem of stability analysis and robust H∞ control for discrete singularly perturbed systems with uncertainty and time-delay is studied. First, a sufficient condition for the existence of a memory state feedback controller is deduced, which can make the closed-loop system meet the H∞ performance index requirement. Because the optimal control theory, Moon inequality and other mathematical methods are used in the derivation process, the H∞ control problem is transformed into a quadratic performance index control problem, which makes the conclusions less conservative. Then, the matrix transformation technique is applied to convert the above conclusions into a MATLAB solvable form, and the parameters of the memory state feedback controller can be obtained by solving the LMI(linear Matrix Inequality). Finally, a corresponding numerical example is given to verify the effectiveness of the control method. © 2023 IEEE.

关键词： linear matrix inequalities

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On the Polyak momentum variants of the greedy deterministic single and multiple row-action methods

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numerical linear algebra WITH applications 2024年第4期31卷 e2552-e2552页

作者： Wu, Nian-Ci Zuo, Qian Wang, Yatian South Cent Minzu Univ Sch Math & Stat Wuhan Peoples R China Peking Univ Ctr Frontiers Comp Studies Beijing Peoples R China Peking Univ Sch Comp Sci Beijing Peoples R China Wuhan Univ Sch Math & Stat Wuhan Peoples R China South Cent Minzu Univ Sch Math & Stat Wuhan 430074 Peoples R China

For solving a consistent system of linear equations, the classical row-action method, such as Kaczmarz method, is a simple while really effective iteration solver. Based on the greedy index selection strategy and Polyak's heavy-ball momentum acceleration technique, we propose two deterministic row-action methods and establish the corresponding convergence theory. We show that our algorithm can linearly converge to a least-squares solution with minimum Euclidean norm. Several numerical studies have been presented to corroborate our theoretical findings. Real-world applications, such as data fitting in computer-aided geometry design, are also presented for illustrative purposes.

关键词： deterministic row-action method greedy index selection strategy momentum real-world applications

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Analysis Directed Design of a Nonlinear, Force-Limiting Composite Shock Isolator for Advanced applications 9

Analysis Directed Design of a Nonlinear, Force-Limiting Comp...

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9th Annual Composites and Advanced Materials Expo, CAMX 2023

作者： Neill, Douglas J. Gosse, Jonathan H. Kanthasamy, Kuna Schneider, Terry L. Computational Engineering Software LLC San AntonioTX78255 United States Composite Technology Concepts LLC PuyallupWA98373 United States

ISBN: (纸本)9781934551448

A novel lightweight, compact shock isolator utilizing composite disc springs was designed using an integrated numerical analysis methodology (Integrated Computational Materials Engineering, ICME). This methodology was used to rapidly screen conceptual designs by guiding material selection, disc geometries and assessment of margins-of-safety (MoS). Current polymer composite disc springs utilize low critical distortional matrix systems. This results in relatively low failure loads requiring stacking multiple discs to increase shock absorbance yielding undesired increases in weight, space and cost. In this study, increased shock absorption was realized by using a higher critical distortional matrix in combination with increased height/thickness ratios for the disc. This enabled a desired nonlinear, "snap-through" behavior of the composite disc requiring non-linear analysis methods and incorporating non-linear contact algorithms. The automated ICME tool was used to generate a desired QZS (quasi-zero stiffness) response within the load-displacement curve for effective shock isolation and determined the required critical material properties of the constituents. A physics-based failure theory was used to determine MoS contour plots. Using the automated ICME tool significantly reduced design cycle-time resulting in testing for validation rather than testing to design. numerical examples are provided demonstrating the utility of the automated ICME tool for designing the innovative shock isolator. Copyright © 2023. Used by CAMX - The Composites and Advanced Materials Expo with permission.

关键词： Matrix algebra

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MULTIDISCIPLINARY OPTIMISATION OF ADDITIVE MANUFACTURED HEAT EXCHANGERS FOR AERONAUTICAL applications 69

MULTIDISCIPLINARY OPTIMISATION OF ADDITIVE MANUFACTURED HEAT...

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69th ASME Turbomachinery Technical conference and Exposition (ASME Turbo Expo) (GT)

作者： Chiodi, Alessandro Alaia, Alessandro Lombardi, Edoardo Cisternino, Marco Gkaragkounis, K. Shahpar, S. Politecn Torino Turin Italy Optimad Engn Turin Italy Rolls Royce Plc Innovat Hub Future Methods London England

ISBN: (纸本)9780791888094

In this work, we investigate a new methodology for the multi-scale simulation and optimisation of Micro Channel Heat Exchangers with lattice-like topology based on homogenization theory. The lattice matrix is modelled as an equivalent porous medium and is simulated only at the macroscale using standard CFD tools. Micro and meso-scale effects are incorporated in terms of variable permeability tensor and heat transfer coefficients, which are assumed to be non-linear functions of the local flow conditions and lattice geometry. Scale bridging is achieved thanks to a Machine Learning (ML) model which is trained to infer the required closure relationships from a database of Direct numerical Simulations (DNS). DNS are performed at the scale of a single lattice cells for several geometries at varying operating conditions. The proposed approach is used to solve a benchmark problem provided by Rolls-Royce plc. The test case involves the optimization of a heat exchanger employed in the cooling system of power electronic. In order to assess the soundness of the proposed methodology, numerical results for three different configurations are presented. The effect of under(over) fitting is also investigated in terms of quality and performances of the final optimal geometry.

关键词： Generative Design Topology Optimisation Multi-fidelity Optimisation Gyroids

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Fixed-time stabilisation of boundary controlled linear parabolic distributed parameter systems with space-dependent reactivity

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IET CONTROL theory AND applications 2021年第5期15卷 652-667页

作者： Bao, Chunxia Cui, Baotong Lou, Xuyang Wu, Wei Zhuang, Bo Jiangnan Univ Sch IoT Engn Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Jiangsu Peoples R China Binzhou Univ Sch Informat Engn Binzhou Peoples R China

The problems of state feedback and output feedback for fixed-time stabilisation of a linear parabolic distributed parameter system with space-dependent reactivity are considered by means of continuous backstepping approach and Lyapunov method. First, the invertible Volterra integral transformation with time dependent gain kernel is adopted to convert the original system into a fixed-time stable target system with time-dependent coefficient. The well-posedness of the resulting kernel equations is proved by the method of successive approximation. Then a state feedback controller is designed to guarantee fixed-time stabilisation of the closed-loop system. Moreover, a fixed-time observer is considered to estimate the state of the original system on the basis of the measurement signal at the boundary. Based on this observer, a observer-based output feedback controller is established to fixed-time stabilise the closed-loop system in a prescribed time by using separation principle. Finally, a numerical simulation is provided to verify the feasibility of the proposed theoretical results by using the modified Ablowitz-Kruskal-Ladik scheme.

关键词： numerical approximation and analysis algebra Mathematical analysis linear control systems Control system analysis and synthesis methods Stability in control theory Distributed parameter control systems Nonlinear control systems

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Algorithmic Gaussianization through Sketching: Converting Data into Sub-gaussian Random Designs 36

Algorithmic Gaussianization through Sketching: Converting Da...

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36th Annual conference on Learning theory (COLT)

作者： Derezinski, Michal Univ Michigan Ann Arbor MI 48109 USA

Algorithmic Gaussianization is a phenomenon that can arise when using randomized sketching or sampling methods to produce smaller representations of large datasets: For certain tasks, these sketched representations have been observed to exhibit many robust performance characteristics that are known to occur when a data sample comes from a sub-gaussian random design, which is a powerful statistical model of data distributions. However, this phenomenon has only been studied for specific tasks and metrics, or by relying on computationally expensive methods. We address this by providing an algorithmic framework for gaussianizing data using sparse sketching operators, proving that it is possible to efficiently construct data sketches that are nearly indistinguishable (in terms of total variation distance) from sub-gaussian random designs. In particular, relying on a recently introduced sketching technique called Leverage Score Sparsified (LESS) embeddings, we show that one can construct an n x d sketch of an N x d matrix A, where n << N, that is nearly indistinguishable from a sub-gaussian design, in time O(nnz(A) log N + nd(2)), where nnz(A) is the number of non-zero entries in A. As a consequence, strong statistical guarantees and precise asymptotics available for the estimators produced from sub-gaussian designs (e.g., for least squares and Lasso regression, covariance estimation, low-rank approximation, etc.) can be straightforwardly adapted to our sketching framework. We illustrate this with a new approximation guarantee for sketched least squares, among other examples. The key technique that enables our analysis is a novel variant of the Hanson-Wright inequality on the concentration of random quadratic forms, which we establish for random vectors that arise from sparse sketches.

关键词： Sketching Least squares Randomized numerical linear algebra Sub-gaussianity

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An iterative algorithm for discrete Lyapunov matrix equations

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IET CONTROL theory AND applications 2021年第16期15卷 2027-2038页

作者： Wu, Ai-Guo Zhang, Ying Sun, Hui-Jie Duan, Hua-Jie Harbin Inst Technol Sch Mech Engn & Automat Shenzhen Peoples R China Sun Yat Sen Univ Sch Aeronaut & Astronaut Guangzhou Peoples R China

In this paper, an iterative algorithm is established to solve discrete Lyapunov matrix equations. In this algorithm, a tuning parameter is introduced such that the iterative solution can be updated by using a combination of the information in the last step and the previous step. Some conditions for the convergence of the proposed algorithm are given. In addition, an approach is also developed to choose the optimal tuning parameter such that the algorithm achieves its fastest convergence rate. A numerical example is employed to illustrate the effectiveness of the proposed algorithm.

关键词： convergence rate iterative algorithm discrete Lyapunov matrix equations linear algebra (numerical analysis) convergence of numerical methods iterative methods numerical analysis Interpolation and function approximation (numerical analysis) optimal tuning parameter Lyapunov matrix equations numerical approximation and analysis

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Improved noise-to-state stability criteria of random nonlinear systems with stochastic impulses

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IET CONTROL theory AND applications 2021年第1期15卷 96-109页

作者： Feng, Likang Park, Ju H. Zhang, Weihai Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Shandong Peoples R China Yeungnam Univ Dept Elect Engn 280 Daehak Ro Kyongsan 38541 South Korea

This paper considers noise-to-state stability for random non-linear systems with stochastic impulses. The impulsive random non-linear systems contain three random characteristics: the second-moment processes in continuous dynamics, the sequence of random variables in discrete dynamics, and the number of stochastic impulses obeyed a renewal process. Firstly, the improved criteria of noise-to-state stability are established for random non-linear systems subject to unstable stochastic impulses based on the uniformly asymptotically stable function. Secondly, improved Lyapunov approaches of NSS with unstable stochastic continuous dynamics are accomplished by the uniformly exponentially stable function. Finally, two numerical examples are used to illustrate the feasibility of the proposed methods.

关键词： Optimisation techniques algebra Other topics in statistics linear control systems Stability in control theory Optimal control Time-varying control systems Distributed parameter control systems Nonlinear control systems

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Flight evaluation of simultaneous actuator/sensor fault reconstruction on a quadrotor minidrone

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IET CONTROL theory AND applications 2021年第16期15卷 2095-2110页

作者： Waitman, S. Alwi, H. Edwards, C. Off Natl Etud & Rech Aerosp French Aerosp Lab DTIS Toulouse France Univ Exeter Coll Engn Math & Phys Sci Exeter EX4 4QF Devon England

In view of the increase in the number of Unmanned Aerial Vehicles (UAVs) in the commercial and private sectors, it is imperative to make sure that such systems are safe, and thus resilient to faults and failures. This paper considers the numerical design and practical implementation of a linear parameter-varying (LPV) sliding mode observer for Fault Detection and Diagnosis (FDD) of a quadrotor minidrone. Starting from a nonlinear model of the minidrone, an LPV model is extracted for design, and the observer synthesis procedure, using linear Matrix Inequalities (LMI), is detailed. Simulations of the observer FDD show good performance. The observer is then implemented on a Parrot(R) Rolling Spider minidrone and a series of flight tests is performed to assess the FDD capabilities in real time using its on-board processing power. The flight tests confirm the performance obtained in simulation, and show that the sliding mode observer is able to provide reliable fault reconstruction for quadrotor minidrone systems.

关键词： algebra Simulation, modelling and identification Control system analysis and synthesis methods Stability in control theory Optimal control Multivariable control systems Nonlinear control systems Aerospace control Mobile robots Telerobotics linear control systems

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Robust state estimation for uncertain linear discrete systems with d-step state delay

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IET CONTROL theory AND applications 2021年第13期15卷 1708-1723页

作者： Wang, Jing Mao, Yao Li, Ziqiang Gao, Junwei Liu, Huabo Qingdao Univ Sch Automat Qingdao 266071 Peoples R China Qingdao Univ Inst Future Qingdao Peoples R China Shandong Key Lab Ind Control Technol Qingdao Peoples R China Chinese Acad Sci Key Lab Opt Engn Chengdu Peoples R China Chinese Acad Sci Inst Opt & Elect Chengdu Peoples R China Univ Chinese Acad Sci Beijing Peoples R China

This paper discusses the state estimation problems of an uncertain linear discrete time-varying state space model with d-step state delay. Based on the principle of minimising the expectation of estimation errors and the method of state augmentation, a robust state estimation algorithm is proposed. Specially, this estimator retains the form of Kalman-like filter and the characteristics of fast recursive calculation. Moreover, the conditions of bounded estimation error covariance and the proof of asymptotic unbiasedness of the filter are given. Finally, numerical examples are used to verify the effectiveness and the wide applicability of this estimator.

关键词： Filtering methods in signal processing Simulation, modelling and identification Other topics in statistics algebra Other topics in statistics linear control systems Control system analysis and synthesis methods Stability in control theory Discrete control systems

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