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A rough logic formalism for fuzzy controllers: A hard and soft computing view

T.Y. Lin
1996 International Journal of Approximate Reasoning  
It starts with a symbolic model that describes the control system in terms of predicates in rough logic.  ...  The collection of all such possible fuzzy worlds is called a rough fuzzy model. It is a highly structured set, and can be treated as a differential geometric object.  ...  ACKNOWLEDGMENTS The author would like to express his deepest thanks to Professor Zadeh for his kind guidance and warm invitation to join the Berkeley Initiative in soft Computing (BISC) group.  ... 
doi:10.1016/s0888-613x(96)00076-x fatcat:6roqxojnand6plzeciurvovgcq

Fuzzy Reasoning and Rough Sets [chapter]

T. Y. Lin
1994 Rough Sets, Fuzzy Sets and Knowledge Discovery  
Modeling of Dynamic Systems Given a set of differential equations, one can model either the solution directly --the theory of differentiable manifolds, or the set of differential equations as an embedded  ...  In classical control (CC), one models the whole systems in which control functions are solutions of system equations, while in fuzzy logic control (FLC), one models the solutions directly.  ... 
doi:10.1007/978-1-4471-3238-7_40 fatcat:zycz6rutxzdutjsg6cgachevpq

Multiscale Modelling of Morphological Evolution of Rough Surface during Superficial, Volume and Evaporation-Condensation Diffusions

M. Bigerelle, Jérôme Favergeon, T. Mathia, Alain Iost
2012 Defect and Diffusion Forum  
An analytical model described by three partial differential equations is built to model time evolution of the surface during heating including three different mechanisms of diffusion: superficial diffusion  ...  Fractal functions are used to model a metallic interface.  ...  Acknowledgements This work was supported by the Région Picardie (France) and the FEDER (Fonds Européen de Développement Régional) in the Project FoncRug3D.  ... 
doi:10.4028/www.scientific.net/ddf.323-325.101 fatcat:jy6o7adl6fhu5kd27igp5qdkkm

Optical scattering simulation of ice particles with surface roughness modeled using the Edwards-Wilkinson equation

Jianing Zhang, Lei Bi, Jianping Liu, R. Lee Panetta, Ping Yang, George W. Kattawar
2016 Journal of Quantitative Spectroscopy and Radiative Transfer  
This paper presents a model for generating surface roughness based on a combination of methods from discrete differential geometry combined with a stochastic partial differential equation for surface evolution  ...  As has been seen in studies using other forms of roughening, the phase function is progressively smoothed as roughness increases.  ...  stochastic partial differential equation. The model makes possible a uniform construction of roughness on particle surfaces that include corners and edges.  ... 
doi:10.1016/j.jqsrt.2016.02.013 fatcat:amds6sn6j5guxbmliyp2bv3rwu

Geometric modeling of aerosol surface roughness and numerical simulation of its impact on aerosol optical properties [article]

Jianing Zhang
2017 arXiv   pre-print
A stochastic method is introduced for geometric modeling aerosol surface roughness with random field and discrete differential geometry theory.  ...  We simulatied scattering phase matrix of model particles, better performace is obtained than smooth particles.  ...  differential equation and finite element.  ... 
arXiv:1704.05821v2 fatcat:av6fw474c5exrmne2g6eqvlile

Usage of a zero-sum differential game in the optimal control of an object described by a nonlinear model

2018 Technical Transactions  
Usage of a zero-sum differential game in the optimal control of an object described by a nonlinear model Wykorzystanie gry różniczkowej o sumie zerowej w optymalnym sterowaniu obiektem opisanym modelem  ...  nieliniowym Abstract This article presents the usage of a zero-sum differential game to control a nonlinear object, which, in the analysed problem, was a mathematical pendulum.  ...  The formal description of such criteria within the confines of modelling is an element of the present study. In this paper, we deal with the optimal robust control.  ... 
doi:10.4467/2353737xct.18.135.8974 fatcat:tivophprxvh6pmqfour4h2ijqy

Rough integrators on Banach manifolds [article]

Ismael Bailleul
2014 arXiv   pre-print
The awaited results on rough differential equations driven by such objects are proved, and a canonical representation is given if the manifold is equipped with a connection.  ...  We introduce a notion of p-rough integrator on any Banach manifolds, for any p≥ 1, which plays the role of weak geometric Holder p-rough paths in the usual Banach space setting.  ...  horizontal rough paths on its frame bundle, and classical weak geometric rough paths on R d , is proved in their setting, using Cartan's development map as an essential ingredient.  ... 
arXiv:1403.3285v3 fatcat:p4fvgquxrncpnlb24hojr3h2ly

Modeling demands for nanoscale devices

M. Pourfath, V. Sverdlov, S. Selberherr
2010 68th Device Research Conference  
In this work we review the approaches to quantum mechanical modeling of carrier transport in nanoscale electronic devices. Numerical analyses for graphene nanoribbons are presented as a case study.  ...  Appropriate technology computer-aided design tools are essential to explore the physics of nanoscale devices and to find methods to optimize their functionality and performance.  ...  The quantum Boltzmann equation is in fact a kinetic differential equation for the Green's function [13] .  ... 
doi:10.1109/drc.2010.5551915 fatcat:mhjpadtqwvec5mtcm3ixbabh3u

Rough integrators on Banach manifolds

I. Bailleul
2019 Bulletin des Sciences Mathématiques  
The awaited results on rough differential equations driven by such objects are proved, and a canonical representation is given if the manifold is equipped with a connection. 1 This research was partially  ...  We introduce a notion of p-rough integrator on any Banach manifolds which plays the role of weak geometric Hölder p-rough paths in the usual Banach space setting, for any p ě 1.  ...  So one can always understand the solution of a rough differential equation driven by a p-rough integrator Θ as the solution to another rough differential equation driven by a p-rough integrator involving  ... 
doi:10.1016/j.bulsci.2018.12.001 fatcat:x5fot2n4onegjkv5jdjodwbooq

The Inverse Problem for Rough Controlled Differential Equations

I. Bailleul, J. Diehl
2015 SIAM Journal of Control and Optimization  
As a first step in rough paths theory, let us consider the controlled ordinary differential equation  ...  Physical examples and applications in stochastic filtering and statistics demonstrate the practical relevance of our result. 2763 2. Rough controlled differential equations.  ...  We shall handle this problem in the model setting of a physical system associated with a rough differential equation, which leads to the following question.  ... 
doi:10.1137/140995982 fatcat:hveqx2t75zbonfwbidoxtoqdk4

The inverse problem for rough controlled differential equations [article]

I. Bailleul, J. Diehl
2014 arXiv   pre-print
We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution.  ...  Physical examples and applications in stochastic filtering and statistics demonstrate the practical relevance of our result.  ...  equations are only measurable functionals of the Brownian path, while rough differential equations can be used to solve Stratonovich differential equations.  ... 
arXiv:1407.2768v3 fatcat:2zntuqcyynajddrjyq6dxczqim

Simplification of control design for driftless nonholonomic systems based on rough path anlaysis

Yûki Nishimura, Kouki Takeuchi
2019 Nonlinear Theory and Its Applications IEICE  
The rough differential equations are allowed to have rough signals generated by unbounded-variation functions and derived by classifying the functions according to "orders" of the boundedness.  ...  The dynamics of the resulting systems are represented by rough differential equations as augmented versions of ordinary differential equations.  ...  The equation is said to be rough differential equations.  ... 
doi:10.1587/nolta.10.431 fatcat:snypg7uvbfffvhf6asrvlolpqa

Convective Heat Transfer in MHD Channels and Its Influence on Channel Performance

R. K. Ahluwalia, E. D. Doss
1980 Journal of Energy  
Validation of Turbulence Model Equation (20) of our roughness model has been previously tested by Cebeci and Chang,12 for incompressible, isothermal rough-wall boundary layer flows.  ...  This turbulence model is used in the differential boundary layer method to relate the turbulent eddy viscosity and conductivity to mean flow quantities.  ... 
doi:10.2514/3.62466 fatcat:adyzhobkpzg27gnwvqdskqedeu

Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast

Liqin Zhang, Xiaojing Tian, Zakariya Chabani
2022 Applied Mathematics and Nonlinear Sciences  
In order to improve the efficiency of dynamic system prediction modelling, this paper proposes a predictive model based on high-order normal differential equations to obtain an explicit model.  ...  The high-order constant differential equation model is reduced, and the numerical method is used to solve the predictive value.  ...  establishment and solving based on high-order normal differential equations Higher-order ordinary differential equation model In the case of known historical data, we calculate the differential differences  ... 
doi:10.2478/amns.2021.2.00114 fatcat:bc5kfcqusbaffl55hwryaryjt4

Discussion: "A General Theory for Laminar Lubrication With Reynolds Roughness" (Elrod, H. G., 1979, ASME J. Lubr. Technol., 101, pp. 8–14)

D. C. Sun
1979 Journal of Lubrication Technology  
In fact, the magnitude of roughness effects depends very much on the roughness autocorrelation function (ACF) and can not be described in gross terms.  ...  The relation between mass flux and mean pressure gradient (B, in the one-dimensional example) can now be used in a differential equation for the mean pressure.  ... 
doi:10.1115/1.3453410 fatcat:rdoazp2ub5hcnno6u5gjpoqixu
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