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New relaxed stability and stabilization conditions for T-S fuzzy systems with time-varying delays

IET CONTROL THEORY AND APPLICATIONS 2021年第14期15卷 1849-1867页

作者： Zhou, Kun Wang, Binrui Qi, Shunan China Jiliang Univ Coll Mech & Elect Engn Hangzhou Peoples R China China Jiliang Univ Coll Modern Sci & Technol Hangzhou Peoples R China

This paper investigates the stability analysis and stabilization of T-S fuzzy systems with time-varying delays. First, a new augmented Lyapunov-Krasovskii functional is constructed, delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) are obtained by combining them with the integral inequality technique and the reciprocally convex combination inequality. Based on the state space decomposition method, some piecewise membership functions are employed to approximate the membership functions. The piecewise membership functions can be locally represented in terms of the convex combinations of the supremum and infimum of some local basis functions. The boundary information of the membership functions is adequately taken into consideration in stability analysis, and then some relaxed membership-function-dependent stability results are obtained. Second, state feedback controllers for fuzzy systems with time-varying delays are presented under the imperfect premise-matching technique, whose membership functions and the number of fuzzy rules are allowed to be designed freely, consequently, the flexibility of controller design is improved. Finally, four numerical examples are given to demonstrate the effectiveness of the presented approaches.

关键词： stabilization conditions convex combinations delay-dependent stability criteria augmented Lyapunov-Krasovskii local basis functions Combinatorial mathematics time-varying systems Time-varying control systems stability control system synthesis Stability in control theory stability analysis Control system analysis and synthesis methods Nonlinear control systems Fuzzy control state feedback state space decomposition method fuzzy systems stability criteria Algebra delays Lyapunov methods integral inequality technique nonlinear control systems fuzzy control linear matrix inequalities reciprocally convex combination inequality time-varying delays relaxed membership-function-dependent stability results piecewise membership functions Distributed parameter control systems fuzzy rules fuzzy set theory

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Active manipulation of Helmholtz scalar fields in an ocean of two homogeneous layers of constant depth

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INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 2021年第13期29卷 2491-2515页

作者： Egarguin, Neil Jerome A. Onofrei, Daniel Qi, Chaoxian Chen, Jiefu Univ Houston Dept Math Houston TX 77204 USA Univ Philippines Los Banos Coll Inst Math Sci & Phys Laguna Philippines Univ Houston Dept Elect & Comp Engn Houston TX USA

In this work, we prove the possibility of actively controlling the acoustic field in an ocean consisting of two homogeneous layers of constant depth using a surface source embedded in one of the layers. For a class of prescribed fields on some bounded control regions in either layer, we show the existence of a boundary input on the source, either acoustic pressure or normal velocity so that the propagated field approximates the prescribed fields. Also, we provide a constructive scheme to find the required boundary input using a Morozov discrepancy principle-based Tikhonov regularization scheme. Several numerical simulations are also provided to support our analyses.

关键词： Acoustic active control scalar Helmholtz fields layered ocean acoustics Tikhonov regularization local basis functions

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Karhunen-Loeve-based approach to tracking of rapidly fading wireless communication channels

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SIGNAL PROCESSING 2023年第1期209卷

作者： Niedzwiecki, Maciej Gancza, Artur Gdansk Univ Technol Fac Elect Telecommun & Comp Sci Dept Automat Control PL-80233 Gdansk Poland

When parameters of wireless communication channels vary at a fast rate, simple estimation algorithms, such as weighted least squares (WLS) or least mean squares (LMS) algorithms, cannot estimate them with accuracy needed to secure reliable operation of the underlying communication systems. In cases like this, the local basis function (LBF) estimation technique can be used instead, significantly increasing the achievable tracking accuracy. We show that when some prior knowledge of statistical properties of parameter changes is available, such as the bandwidth of their variation, both the type and the number of basis functions, used in the LBF approach to approximate time-varying channel parameters, can be optimized using the Karhunen-Loeve (KL) decomposition based technique. (c) 2023 Elsevier B.V. All rights reserved.

关键词： Time -varying channels local basis functions Karhunen-Lo?ve expansion

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local-basis difference potentials method for elliptic PDEs in complex geometry

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JOURNAL OF COMPUTATIONAL PHYSICS 2023年第1期488卷

作者： Xia, Qing KTH Royal Inst Technol Dept Math Stockholm Sweden

We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the difference potentials framework. The main novelty of the developed schemes is the use of local basis functions defined at near -boundary grid points. The use of local basis functions allows unified numerical treatment of (i) explicitly and implicitly defined geometry;(ii) geometry of more complicated shapes, such as those with corners, multi-connected domain, etc;and (iii) different types of boundary conditions. This geometrically flexible approach is complementary to the classical difference potentials method using global basis functions, especially in the case where a large number of global basis functions are needed to resolve the boundary, or where the optimal global basis functions are difficult to obtain. Fast Poisson solvers based on FFT are employed for standard, centered finite difference stencils regardless of the designed order of accuracy. Proofs of convergence of difference potentials in maximum norm are outlined both theoretically and numerically.& COPY;2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

关键词： Difference potentials Fast Poisson solver Geometric flexibility High-order finite difference local basis functions

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Interpolating splines on graphs for data science applications

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2020年第2期49卷 540-557页

作者： Ward, John Paul Narcowich, Francis J. Ward, Joseph D. North Carolina A&T State Univ Greensboro NC 27411 USA Texas A&M Univ College Stn TX USA

We introduce intrinsic interpolatory bases for data structured on graphs and derive properties of those bases. Polyharmonic Lagrange functions are shown to satisfy exponential decay away from their centers. The decay depends on the density of the zeros of the Lagrange function, showing that they scalewith the density of the data. These results indicate that Lagrange-type bases are ideal building blocks for analyzing data on graphs, and we illustrate their use in kernel-based machine learning applications. (C) 2020 Elsevier Inc. All rights reserved.

关键词： local basis functions Kernel-based machine learning Interpolation Lagrange functions

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local basis function representations of thermodynamic surfaces: Water at high pressure and temperature as an example

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FLUID PHASE EQUILIBRIA 2018年 463卷 18-31页

作者： Brown, J. Michael Univ Washington Dept Earth & Space Sci Box 35-1310 Seattle WA 98195 USA

A flexible numerical framework using local basis function is developed in order to better represent thermodynamic properties of fluids as a function of pressure temperature and composition. A new equation of state for water to 100 GPa and 10,000 K is presented. Conventional equations of state are typically based on complex sets of global basis functions that are unique to each application. The use of series expansions in positive and negative powers of the independent variables (with additional exponential/log/trig. factors in some cases) is common and recent accurate equations of state are assembled from collections of such arbitrary terms. These individually crafted representations do not always fit data within uncertainties, can be difficult to implement, and are not easily modified to account for newer data. Multivariate (tensor) b splines overcome these shortcomings. The underlying basis functions are local, orthonormal and complete. Data can be represented to arbitrary precision and the relationships between model parameters and observational constraints are uncomplicated. The fittings of new data in more extended regimes of the thermodynamic space do not require modifying parameters in previously constrained regions. Models are transportable and easily implemented since robust and efficient standardized routines for evaluation of b splines are available in modern numerical environments. Because a local basis function representation can flexibly fit any surface, the articulation of a priori constraints (associated with expected physical and chemical behavior) is appropriately necessary and explicit during model construction. Basic tools are demonstrated in applications to thermodynamic properties of water where the modified equation of state matches a prior formulation below 1 GPa while providing an excellent fit to measurements at much higher pressures. (C) 2018 Elsevier B.V. All rights reserved.

关键词： b spline local basis functions Equation of state Fluid thermodynamics Regularized parameter estimation Water

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Constraint Energy Minimizing Generalized Multiscale Finite Element Method

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2018年第Sep.1期339卷 298-319页

作者： Chung, Eric T. Efendiev, Yalchin Leung, Wing Tat Chinese Univ Hong Kong Dept Math Hong Kong Hong Kong Peoples R China Texas A&M Univ Dept Math College Stn TX 77843 USA Texas A&M Univ Inst Sci Computat College Stn TX USA

In this paper, we propose Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM). The main goal of this paper is to design multiscale basis functions within GMsFEM framework such that the convergence of method is independent of the contrast and linearly decreases with respect to mesh size if oversampling size is appropriately chosen. We would like to show a mesh-dependent convergence with a minimal number of basis functions. Our construction starts with an auxiliary multiscale space by solving local spectral problems. In auxiliary multiscale space, we select the basis functions that correspond to small (contrast-dependent) eigenvalues. These basis functions represent the channels (high-contrast features that connect the boundaries of the coarse block). Using the auxiliary space, we propose a constraint energy minimization to construct multiscale spaces. The minimization is performed in the oversampling domain, which is larger than the target coarse block. The constraints allow handling non-decaying components of the local minimizers If the auxiliary space is correctly chosen, we show that the convergence rate is independent of the contrast (because the basis representing the channels are included in the auxiliary space) and is proportional to the coarse-mesh size (because the constraints handle non-decaying components of the local minimizers). The oversampling size weakly depends on the contrast as our analysis shows. The convergence theorem requires that channels are not aligned with the coarse edges, which hold in many applications, where the channels are oblique with respect to the coarse-mesh geometry. The numerical results confirm our theoretical results. In particular, we show that if the oversampling domain size is not sufficiently large, the errors are large. To remove the contrast-dependence of the oversampling size, we propose a modified construction for basis functions and present numerical results and the analysis. (C) 201

关键词： Generalized multiscale finite element method High contrast flow local basis functions

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Mercury's global topography and tidal signal from laser altimetry by using a rectangular grid

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PLANETARY AND SPACE SCIENCE 2010年第14-15期58卷 2022-2030页

作者： Koch, Christian Kallenbach, Reinald Christensen, Ulrich Max Planck Inst Sonnensyst Forsch D-37191 Katlenburg Lindau Germany

Laser altimeters on board the MESSENGER and BepiColombo missions will accurately map Mercury's topography including the time-dependent elevation from solar tides, which are predicted to be of order 1 m. The amplitude of solar tides, characterized by the Love number h(2), reveals information on the interior structure of Mercury, in particular on the state and the size of the core. Koch et al., [Koch et al., (2008). Planet. Space Sci. 56, 1226-1237] have directly decomposed a global synthetic altimetry record into the time-dependent tidal signal and into a spherical harmonic expansion of the static topography. The precision for h(2) depends on the maximum degree l of the expansion which is practically limited because the computation time increases very strongly with I. Here, we show that the computation time to achieve the same precision can be substantially reduced if we describe the static topography in terms of local basis functions defined on a rectangular grid. The subsequent projection of the grid data onto the orthonormal spherical harmonic functions is very rapid. The new method is promising to achieve high precision to test current models of Mercury's interior and additionally delivers a topographic map with approximately 4.7 million grid points. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： BepiColombo Mercury Tidal Love number Rectangular grid Long-wavelength topography local basis functions

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Getting weights to behave themselves: Achieving stability and performance in neural-adaptive control when inputs oscillate

Getting weights to behave themselves: Achieving stability an...

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American Control Conference 2005 (ACC)

作者： Macnab, CJB Univ Calgary Dept Elect & Comp Engn Calgary AB Canada

ISBN: (纸本)0780390989

local basis functions offer computational efficiency when used in nonlinear adaptive control schemes. However, commonly used robust weight (parameter) update methods do not result in acceptable performance when applied to underdamped systems. This is because persistent oscillation in the inputs encourages severe weight drift, in turn requiring large robust terms that significantly limit the performance. In particular, the methods of leakage, e-modification, deadzone, and weight projection sacrifice performance to halt this weight drift. In contrast, it is observed (in simulations) that application of the proposed method halts the weight drift without sacrificing the performance.

关键词： direct adaptive control nonlinear approximate control neural network control fuzzy control Lyapunov stability local basis functions beta-splines CMAC

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