共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, Multiquadric quasi-interpolation method is used to approximate fractional integral equations and fractional differential equations.
Firstly, we construct two operators for approximating the Hadamard integral-differential equation based on quasi interpolators, and verify their properties and order of convergence. Secondly, we obtain that the approximation order of the integral scheme is 3, and the approximation order of the differential scheme is $3-\mu$ for $\mu(0<\mu<1)$ order fractional Hadamard derivative. Finally, The results of numerical experiments show that the numerical results are in greement with the theoretical analysis. 相似文献
2.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(9):2235-2244
In recent years piecewise affine (PWA) modeling has developed as an attractive tool for the approximation of various complex nonlinear systems. In spite of the wide application of PWA modeling, the optimal approximation of a continuous time nonlinear system with scalar functions by the minimum number of affine systems has not been addressed properly in literature. This paper deals with a fuzzy clustering based approach for the optimal PWA approximation of a class of continuous time nonlinear systems. The technique is based on the trade-off between increasing the approximation accuracy of the various nonlinear functions and simplifying the approximation by the minimum number of subsystems. As an application, the technique is utilized to obtain a PWA approximation of the glucose regulation system. Numerical simulations depicted that, for a given number of subsystems, the derived glucose regulation model provides an optimal approximation of the original nonlinear system. The model also provided some biological insight about the interactions involved in glucose regulation. 相似文献
3.
Summary. In this work, new interpolation error estimates have been derived for some well-known interpolators in the quasi-norms. The estimates are found to be essential to obtain the optimal a priori error bounds under the weakened regularity conditions for the piecewise linear finite element approximation of a class of degenerate equations. In particular, by using these estimates, we can close the existing gap between the regularity required for deriving the optimal error bounds and the regularity achievable for the smooth data for the 2-d and 3-d p-Laplacian.Mathematics Subject Classification (1991): 65N30 相似文献
4.
G. Grammel 《PAMM》2003,2(1):412-413
The Takens equation for modeling strong elastic constraints in mechanical systems is considered. Using averaging techniques, approximation orders for “passing through resonance” problems are provided. For “thick” resonance sets, the relevance of third order resonances is shown via a multi‐valued averaging approach. 相似文献
5.
A novel scheme is proposed for the design of backstepping control for a class of state-feedback nonlinear systems. In the design, the unknown nonlinear functions are approximated by the neural networks (NNs) identification models. The Lyapunov function of every subsystem consists of the tracking error and the estimation errors of NN weight parameters. The adaptive gains are dynamically determined in a structural way instead of keeping them constants, which can guarantee system stability and parameter estimation convergence. When the modeling errors are available, the indirect backstepping control is proposed, which can guarantee the functional approximation error will converge to a rather small neighborhood of the minimax functional approximation error. When the modeling errors are not available, the direct backstepping control is proposed, where only the tracking error is necessary. The simulation results show the effectiveness of the proposed schemes. 相似文献
6.
Linking structural equation modeling to Bayesian networks: Decision support for customer retention in virtual communities 总被引:1,自引:1,他引:0
Bayesian networks are limited in differentiating between causal and spurious relationships among decision factors. Decision making without differentiating the two relationships cannot be effective. To overcome this limitation of Bayesian networks, this study proposes linking Bayesian networks to structural equation modeling (SEM), which has an advantage in testing causal relationships between factors. The capability of SEM in empirical validation combined with the prediction and diagnosis capabilities of Bayesian modeling facilitates effective decision making from identification of causal relationships to decision support. This study applies the proposed integrated approach to decision support for customer retention in a virtual community. The application results provide insights for practitioners on how to retain their customers. This research benefits Bayesian researchers by providing the application of modeling causal relationships at latent variable level, and helps SEM researchers in extending their models for managerial prediction and diagnosis. 相似文献
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We consider time semi-discrete approximations of a class of exponentially stable infinite-dimensional systems modeling, for instance, damped vibrations. It has recently been proved that for time semi-discrete systems, due to high frequency spurious components, the exponential decay property may be lost as the time step tends to zero. We prove that adding a suitable numerical viscosity term in the numerical scheme, one obtains approximations that are uniformly exponentially stable. This result is then combined with previous ones on space semi-discretizations to derive similar results on fully-discrete approximation schemes. Our method is mainly based on a decoupling argument of low and high frequencies, the low frequency observability property for time semi-discrete approximations of conservative linear systems and the dissipativity of the numerical viscosity on the high frequency components. Our methods also allow to deal directly with stabilization properties of fully discrete approximation schemes without numerical viscosity, under a suitable CFL type condition on the time and space discretization parameters. 相似文献
10.
Stefan Mittnik Irina Starobinskaya 《Methodology and Computing in Applied Probability》2010,12(3):379-390
This paper addresses the problem of quantifying and modeling financial institutions’ operational risk in accordance with the
Advanced Measurement Approach put forth in the Basel II Accord. We argue that standard approaches focusing on modeling stochastic
dependencies are not sufficient to adequately assess operational risk. In addition to stochastic dependencies, causal topological
dependencies between the risk classes are typically encountered. These dependencies arise when risk units have common information-
and/or work-flows and when failure of upstream processes imply risk for downstream processes. In this paper, we present a
modeling strategy that explicitly captures both topological and stochastic dependencies between risk classes. We represent
the operational-risk taxonomy in the framework of a hybrid Bayesian network (BN) and provide an intuitively compelling approach
for handling causal relationships and external influences. We demonstrate the use of hybrid BNs as a tool for mapping causal
dependencies between frequencies and severities of risk events and for modeling common shocks. Monte-Carlo simulations illustrate
that the impact of topological dependencies on triggering overall system breakdowns can be substantial. 相似文献
11.
《International Journal of Approximate Reasoning》2007,44(1):32-44
The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. An important characteristic that distinguishes fuzzy systems from other techniques in this area is their transparency and interpretability. Especially in the construction of a fuzzy system from a set of given training examples, little attention has been paid to the analysis of the trade-off between complexity and accuracy maintaining the interpretability of the final fuzzy system. In this paper a multi-objective evolutionary approach is proposed to determine a Pareto-optimum set of fuzzy systems with different compromises between their accuracy and complexity. In particular, two fundamental and competing objectives concerning fuzzy system modeling are addressed: fuzzy rule parameter optimization and the identification of system structure (i.e. the number of membership functions and fuzzy rules), taking always in mind the transparency of the obtained system. Another key aspect of the algorithm presented in this work is the use of some new expert evolutionary operators, specifically designed for the problem of fuzzy function approximation, that try to avoid the generation of worse solutions in order to accelerate the convergence of the algorithm. 相似文献
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13.
Leon Lasdon 《Annals of Operations Research》2001,105(1-4):99-107
Great strides have been made in nonlinear programming (NLP) in the last 5 years. In smooth NLP, there are now several reliable and efficient codes capable of solving large problems. Most of these implement GRG or SQP methods, and new software using interior point algorithms is under development. NLP software is now much easier to use, as it is interfaced with many modeling systems, including MSC/NASTRAN, and ANSYS for structural problems, GAMS and AMPL for general optimization, Matlab and Mathcad for general mathematical problems, and the widely used Microsoft Excel spreadsheet. For mixed integer problems, branch and bound and outer approximation codes are now available and are coupled to some of the above modeling systems, while search methods like Tabu Search and Genetic algorithms permit combinatorial, nonsmooth, and nonconvex problems to be attacked. 相似文献
14.
In this work multiscale failure modeling of composites is made using generalized finite element method (GFEM). In this method the global approximation are constructed by combining the local basis with partition of unity functions. The enrichment functions for the GFEM approximation are computed using a proper orthogonal decomposition (POD) technique. The approximation is then used in a two scale Galerkin scheme for failure modeling of composites. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
《European Journal of Operational Research》1999,117(1):63-83
An original methodology for using rough sets to preference modeling in multi-criteria decision problems is presented. This methodology operates on a pairwise comparison table (PCT), including pairs of actions described by graded preference relations on particular criteria and by a comprehensive preference relation. It builds up a rough approximation of a preference relation by graded dominance relations. Decision rules derived from the rough approximation of a preference relation can be used to obtain a recommendation in multi-criteria choice and ranking problems. The methodology is illustrated by an example of multi-criteria programming of water supply systems. 相似文献
16.
Anatoli Torokhti Phil Howlett Charles Pearce 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(3):327-343
We propose a new method for the optimal causal representation of nonlinear systems. The proposed approach is based on the best constrained approximation of mappings in probability spaces by operators constructed from matrices of special form so that the approximant preserves the causality property. It is supposed that the observable input is contaminated with noise. The approximant minimises the mean-square difference between a desired output signal and the output signal of the approximating model. The method provides a numerically realisable mathematical model of the system. An analysis is given of the error associated with this representation. 相似文献
17.
In this paper, we propose a robust anti-synchronization scheme based on multiple-kernel least squares support vector machine (MK-LSSVM) modeling for two uncertain chaotic systems. The multiple-kernel regression, which is a linear combination of basic kernels, is designed to approximate system uncertainties by constructing a multiple-kernel Lagrangian function and computing the corresponding regression parameters. Then, a robust feedback control based on MK-LSSVM modeling is presented and an improved update law is employed to estimate the unknown bound of the approximation error. The proposed control scheme can guarantee the asymptotic convergence of the anti-synchronization errors in the presence of system uncertainties and external disturbances. Numerical examples are provided to show the effectiveness of the proposed method. 相似文献
18.
一类用于复杂系统Fuzzy控制的因果关系归纳推理机制 总被引:5,自引:0,他引:5
本文以复杂系统的Fuzzy控制为背景,在Fuzzy语言场与Fuzzy语言值结构的描述架下,构造了一类在大范围内适用的因果关系归纳推理机制,并找到了它在Fuzzy控制中的应用。 相似文献
19.
M. Tadi 《Applied Mathematics and Optimization》1997,35(3):331-351
This paper is concerned with modeling and control of a multicomponent distributed-parameter structure. General results from
the theory of infinitedimensional systems are used to pose an LQR-control problem for the structure. Different variations
of the structure are considered and, in particular, approximation schemes for two forms of the structure are presented in
detail. Responses of the system to an elastic initial condition are presented. It is shown that convergent state feedback
control laws can be obtained which result in significant suppression of vibrations and unwanted displacements throughout the
structure. 相似文献
20.
We provide existence results for nonnegative solutions to a class of reaction-diffusion systems with cross-diffusion modeling
the spread of an epidemic disease. The existence of weak solutions is proved by means of an approximation process, the Faedo-Galerkin
method, and a compactness argument. Under additional assumptions a global existence result for classical solutions is derived
upon using interpolation results between Banach spaces. 相似文献