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Unidentified Input Observer using orthogonal Hybrid function

IFAC-PapersOnLine 2018年第1期51卷 255-260页

作者： Ghosh, Aniruddha Ghosh, Anindya Ganguly, Anindita Chatterjee, Saumya Deep Dhanbad India Department of Mechanical Engineering MCKV Institute of Engineering Howrah India Department of Electrical Engineering St. Thomas’ College of Engineering & Technology Kolkata India

In practice, it is often the case that systems can be modeled as having unidentified inputs. In order to achieve certain control objectives, it may be necessary to estimate the inputs and states for such systems. The general approach used for such problems is the use of coordinate transformation. In this paper we are using orthogonal hybrid functions to estimate both the state vectors and the unidentified inputs for a given system. The method of expansion using hybrid function and its derived differential operation are presented to alleviate such problems from an algebraic form. Our design procedure is quite general as it encompasses the design of Unidentified Input Observers via appropriate choices of design matrices. For the existence of such observers we are providing necessary and sufficient conditions. © 2018

关键词： Orthogonal functions Algebra Sampling State space methods Algebraic approaches Co ordinate transformation Control objectives Design procedure Differential operation Hold function Hybrid functions triangular functions

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Optimal control of Volterra integral equations via triangular functions

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MATHEMATICAL AND COMPUTER MODELLING 2011年第9-10期53卷 1902-1909页

作者： Maleknejad, K. Almasieh, H. Islamic Azad Univ Karaj Branch Dept Math Karaj Iran Islamic Azad Univ Dept Math Khorasgan Branch Esfahan Iran

This paper presented an approximate method for solving optimal control problem of Volterra integral equations. The method is based upon orthogonal triangular functions. The error estimates and associated theorems have been proved for optimal control and cost functionals. Some numerical examples illustrate the efficiency of the proposed method. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Volterra integral equations Optimal control triangular functions

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triangular functions (TF) method for the solution of nonlinear Volterra-Fredholm integral equations

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2010年第11期15卷 3293-3298页

作者： Maleknejad, K. Almasieh, H. Roodaki, M. Islamic Azad Univ Dept Math Sci & Res Branch Tehran Iran

A numerical method based on an m-set of general, orthogonal triangular functions (TF) is proposed to approximate the solution of nonlinear Volterra-Fredholm integral equations. The orthogonal triangular functions are utilized as a basis in collocation method to reduce the solution of nonlinear Volterra-Fredholm integral equations to the solution of algebraic equations. Also a theorem is proved for convergence analysis Some numerical examples illustrate the proposed method (C) 2009 Elsevier B V All rights reserved

关键词： Integral equations Nonlinear triangular functions Volterra-Fredholm

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National economies in state-space of fractional-order financial system

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AFRIKA MATEMATIKA 2016年第3-4期27卷 529-540页

作者： Fazli, H. Rahmani Hassani, F. Ebadian, A. Khajehnasiri, A. A. Shahid Beheshti Univ Fac Econ & Polit Dept Econ Tehran Iran Payame Noor Univ Dept Math POB 19395-3697 Tehran Iran

In this paper, we present a method for solving national economies in state space with fractional order, we use the triangular function operational matrix of the fractional order integration to solve the fractional-order national economies equation. The method is described and illustrated with numerical simulation. Numerical simulations are given to verify the effectiveness of the proposed method.

关键词： National economies State-space triangular functions Operational matrix Fractional calculus Block pulse function

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Numerical solution of multi-order fractional differential equations using generalized triangular function operational matrices

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APPLIED MATHEMATICS AND COMPUTATION 2015年 263卷 189-203页

作者： Damarla, Seshu Kumar Kundu, Madhusree Natl Inst Technol Dept Chem Engn Rourkela 769008 Odisha India

Most fractional differential equations do not have closed form solutions. Development of effective numerical techniques has been an interesting research topic for decades. In this context, this paper proposes a numerical technique, for solving linear and nonlinear multi-order fractional differential equations, based on newly computed generalized triangular function operational matrices for Riemann-Liouville fractional order integral. The orthogonal triangular functions are evolved from a simple dissection of piecewise constant orthogonal block pulse functions. Theoretical error analysis is performed to estimate the upper bound of absolute error between the exact Riemann-Liouville fractional order integral and its approximation in the triangular functions domain. Numerical examples are considered for investigating the applicability and effectiveness of proposed technique to solve multi-order fractional differential equations. The results encourage the use of orthogonal TFs for analysis of real processes exhibiting fractional dynamics. (C) 2015 Published by Elsevier Inc.

关键词： triangular functions Multi-order fractional differential equations Riemann-Liouville fractional integral

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Solution of nonlinear fractional diffusion-wave equation by traingular functions

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SeMA Journal 2015年第1期72卷 37-46页

作者： Ebadian, A. Fazli, H. Rahmani Khajehnasiri, A.A. Department of Mathematics Payame Noor University PO Box 19395-3697 Tehran Iran Department of Economic Faculty of Economic and Political Shahid Beheshti University Tehran Iran

In this paper, we propose new technique for solving fractional diffusion-wave equation. This algorithm is based on triangular Function (TFs) methods, a new fractional operational matrix of integration for the TFs is derived. The TFs and their fractional operational matrix of integration are used to transform the problem under consideration into a linear system of algebraic equations. The new technique is applied to solving two mathematical models. We show that the present approach is relatively easy, efficient and highly accurate. © 2015, Sociedad Española de Matemática Aplicada.

关键词： Block pulse function Fractional calculus Fractional diffusion-wave equation Operational matrix triangular functions

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Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2009年第2期58卷 239-247页

作者： Babolian, E. Masouri, Z. Hatamadeh-Varmazyar, S. Islamic Azad Univ Dept Math Sci & Res Branch Tehran Iran Islamic Azad Univ Dept Elect Engn Sci & Res Branch Tehran Iran

An effective direct method to determine the numerical solution of the specific nonlinear Volterra-Fredholm integro-differential equations is proposed. The method is based on new vector forms for representation of triangular functions and its operational matrix. This approach needs no integration, so all calculations can be easily implemented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method. (c) 2009 Elsevier Ltd. All rights reserved.

关键词： Nonlinear integro-differential equations Direct method Vector forms triangular functions Operational matrix

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Recursive Linear and Differential Cryptanalysis of Ultralightweight Authentication Protocols

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2013年第7期8卷 1140-1151页

作者： Ahmadian, Zahra Salmasizadeh, Mahmoud Aref, Mohammad Reza Sharif Univ Technol Dept Elect Engn ISSL Tehran *** Iran Sharif Univ Technol Elect Res Inst Tehran *** Iran

Privacy is faced with serious challenges in the ubiquitous computing world. In order to handle this problem, some researchers in recent years have focused on design and analysis of privacy-friendly ultralightweight authentication protocols. Although the majority of these schemes have been broken to a greater or lesser extent, most of these attacks are based on ad-hoc methods that are not extensible to a large class of ultralightweight protocols. So this research area still suffers from the lack of structured cryptanalysis and evaluation methods. In this paper, we introduce new frameworks for full disclosure attacks on ultralightweight authentication protocols based on new concepts of recursive linear and recursive differential cryptanalysis. The recursive linear attack is passive, deterministic, and requires only a single authentication session, if it can be applied successfully. The recursive differential attack is more powerful and can be applied to the protocols on which the linear attack may not work. This attack is probabilistic, active in the sense that the attacker suffices only to block some specific messages, and requires a few authentication sessions. Having introduced these frameworks in a general view, we apply them on some well-known ultralightweight protocols. The first attack can retrieve all the secret data of Yeh et al. and SLMAP authentication protocols and the second one can retrieve all the secret data of LMAP(++), SASI, and David-Prasad authentication protocols.

关键词： RFID technology system of linear equations triangular functions ultralightweight authentication protocols

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A Dual Purpose triangular Neural Network Based Module for Monitoring and Protection in Bi-Directional Off-Board Level-3 Charging of EV/PHEV

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IEEE TRANSACTIONS ON SMART GRID 2012年第4期3卷 1670-1678页

作者： Lu, Xiaomin Iyer, K. Lakshmi Varaha Mukherjee, Kaushik Kar, Narayan C. Univ Windsor Ctr Hybrid Automot Res & Green Energy Windsor ON N9B 3P4 Canada

Understanding the need for improvement in monitoring and protection in high performance charging technology for a growing demand of EVs/PHEVs, this research manuscript presents a part of an ongoing project and proposes a novel low cost dual purpose triangular neural network based module for power quality monitoring and protection (M&P) and elicits its performance in times of abnormalities or malfunction in a high performance off-board level 3 bi-directional charger for electric vehicles. Firstly, design and implementation of the low cost dual purpose triangular neural network based device for monitoring the power quality and hence, protecting the grid has been explained and its performance has been presented through numerical investigations. Going a step further, the device has also been experimentally tested using an in-house electric vehicle containing a commercially available battery charger and the measured results are analyzed. Secondly, a high-performance vector-controlled bi-directional off-board level-3 charger for faster and efficient charging has been developed and investigations have been performed on the healthy charger to analyze its performance. The primary aim of developing this charger was to elicit the usage and performance of the previously developed M&P device to protect the grid in case of some typical charger malfunction problem in such a charger, which is not detectable by conventional low cost sensors employed with such chargers. Once the module detects any abnormalities in the charger's operation, information gathered can be used to tune the controller in the charger to obtain a constant improved performance of the charger or the power transfer can be terminated.

关键词： Artificial neural network bi-directional off-board level-3 charger electric vehicles monitoring and protection plug-in hybrid electric vehicles triangular functions

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Numerical solution of third order linear differential equations using generalized one-shot operational matrices in orthogonal hybrid function domain

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APPLIED MATHEMATICS AND COMPUTATION 2012年第4期219卷 1485-1514页

作者： Deb, Anish Ganguly, Anindita Sarkar, Gautam Biswas, Amitava Jadavpur Univ Dept Mech Engn Kolkata 700032 India Univ Calcutta Dept Appl Phys Kolkata 700009 W Bengal India Acad Technol Dept Elect Engn Hooghly India

The present work proposes a new set of orthogonal hybrid functions (HF) which evolved from synthesis of orthogonal sample-and-hold functions (SHF) and triangular functions (TF). The HF set is used to approximate a time function in a piecewise linear manner. For such approximation, the mean integral square error (MISE) is much less than block pulse function based approximation which always provides staircase solutions and it is found that HF based approximation is a strong contender of approximations based upon orthogonal polynomials like Legendre polynomials. The respective MISE's and elapsed times for MISE computations for these three kinds of approximations are also studied in detail. The one-shot operational matrices for integration of different orders in HF domain are also derived. These matrices are employed for more accurate multiple integration. An example is treated to determine efficiency of these matrices. Finally, these matrices are employed for solving third order non-homogeneous differential equations followed by a numerical example. The results, obtained via MATLAB, are compared with the exact solution as well as the results obtained via 4th order Runge-Kutta method. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Sample-and-hold functions triangular functions Hybrid functions Function approximation Operational matrices Differential equation

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