This article proposes an efficient method for solving stochastic Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, a stochastic Volterra integral equat...
详细信息
This article proposes an efficient method for solving stochastic Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, a stochastic Volterra integral equation can be reduced to a linear lower triangular system, which can be directly solved by forward substitution. The results show that the approximate solutions have a good degree of accuracy. (C) 2011 Elsevier Ltd. All rights reserved.
When there are time-varying parameters in motion equations, the optimal guidance law with multi-constraints generally cannot be solved analytically. Based on block pulse functions, a design method of optimal guidance ...
详细信息
When there are time-varying parameters in motion equations, the optimal guidance law with multi-constraints generally cannot be solved analytically. Based on block pulse functions, a design method of optimal guidance law is presented combining optimal control theory and numerical value computation for time-varying systems. The presented guidance law can optimize the combination of landing angle, miss distance, and control energy consumption. Using both the proposed guidance law and the proportional navigation law, ballistic simulations are made. Compared to the proportional navigation law, the optimal guidance law is able to more than double the landing angle. Because of the steep terminal trajectory, the strike accuracy and damage effects are increased. Averaging the time-varying coefficients of the optimal guidance law, a suboptimal guidance law is obtained. This guidance law is simpler and can make the terminal trajectory steep too. Therefore, it could be applied to projects more easily and requires less onboard computational resources. However, it consumes slightly more control energy than the optimal guidance law. (C) 2011 Elsevier Masson SAS. All rights reserved.
A nonlinear operational matrix is derived via Legendre polynomials (LPs) and block pulse functions (BPFs). Using the nonlinear operationalmatrix and other relevant operational properties of LPs and BPFs, an approximat...
详细信息
A nonlinear operational matrix is derived via Legendre polynomials (LPs) and block pulse functions (BPFs). Using the nonlinear operationalmatrix and other relevant operational properties of LPs and BPFs, an approximate solution for a nonlinear optimal control problem with quadratic performance index is given. Three illustrative examples are included to demonstrate the validity of the proposed approach.
This paper proposes the equivalent linearization (EL) and sliding mode control (SMC) methods to address nonlinearity and enhance the performance of nonlinear systems subjected to nonstationary random excitations. The ...
详细信息
This paper proposes the equivalent linearization (EL) and sliding mode control (SMC) methods to address nonlinearity and enhance the performance of nonlinear systems subjected to nonstationary random excitations. The EL methods are commonly used to propose approximate solutions for nonlinear systems under random excitations due to the high computational demands in the exact analyses. Considering the application of orthogonal functions in improving the accuracy and efficiency of approximate solutions, an orthogonal blockpulse (BP) function is applied to the EL method in this study to approximate the nonlinear system responses under nonstationary random excitations. The SMC, as a robust control method for systems with uncertainties and external disturbances, is capable of achieving reliable and accurate tracking control. This method is applied to effectively reduce the dynamic responses predicted by the proposed EL method under nonstationary random excitations. The proposed approach is tested on single-degree-of-freedom and two-degree-of-freedom Duffing systems subjected to a seismic type excitation. The results indicate that not only the orthogonal function-based EL method can approximate the dynamic responses more accurately, at lower computational cost, and by a high agreement with the exact solution, but also the proposed SMC can improve the performance of nonlinear systems by effectively reducing the responses compared with the linear quadratic regulator control method.
In this paper, the block pulse functions (BPFs) and their operational matrix are used to solve two-dimensional Fredholm-Volterra integral equations (F-VIE). This method converts F-VIE to systems of linear equations wh...
详细信息
In this paper, the block pulse functions (BPFs) and their operational matrix are used to solve two-dimensional Fredholm-Volterra integral equations (F-VIE). This method converts F-VIE to systems of linear equations whose solutions are the coefficients of blockpulse expansions of the solutions of F-VIE. Finally some numerical examples are presented to show the efficiency and accuracy of the method. (C) 2011 Published by Elsevier B.V.
In this paper a modification of block pulse functions is introduced and used to solve Volterra integral equation of the first kind. Some theorems are included to show convergence and advantage of the method. Some exam...
详细信息
In this paper a modification of block pulse functions is introduced and used to solve Volterra integral equation of the first kind. Some theorems are included to show convergence and advantage of the method. Some examples show accuracy of the method. (C) 2010 Elsevier B.V. All rights reserved.
This article proposes a simple efficient method for solving a Volterra integral equations system of the first kind. By using block pulse functions and their operational matrix of integration, a first kind integral equ...
详细信息
This article proposes a simple efficient method for solving a Volterra integral equations system of the first kind. By using block pulse functions and their operational matrix of integration, a first kind integral equations system can be reduced to a linear system of algebraic equations. The coefficient matrix of this system is a block matrix with lower triangular blocks. Numerical examples show that the approximate solutions have a good degree of accuracy.
A method for finding the optimal control of linear fractional-order singular systems with a quadratic cost functional using block pulse functions is discussed. By using the operational properties of orthogonal functio...
详细信息
ISBN:
(纸本)9781467311496
A method for finding the optimal control of linear fractional-order singular systems with a quadratic cost functional using block pulse functions is discussed. By using the operational properties of orthogonal functions, computationally attractive algorithms are developed for calculating optimal control law and state variable of dynamical system. A numerical example is included to demonstrate the validity and the applicability of the technique.
In this study, a new representation formula for basic functions of fuzzy transform is introduced and some new approximating properties of the inverse fuzzy transform are described. In particular, using blockpulse fun...
详细信息
In this study, a new representation formula for basic functions of fuzzy transform is introduced and some new approximating properties of the inverse fuzzy transform are described. In particular, using block pulse functions, we present properties of sinusoidal basic functions. As an application, we present a new fuzzy-based method for numerical solution of nonlinear Fredholm integral equations.
In this paper, we give a brief review on block pulse functions (BPFs) and obtain operational matrix and stochastic operational matrix of integration based on BPFs. Then these operational matrices are used to solve sys...
详细信息
In this paper, we give a brief review on block pulse functions (BPFs) and obtain operational matrix and stochastic operational matrix of integration based on BPFs. Then these operational matrices are used to solve system of linear Stratonovich Volterra integral equations. By applying proposed method, the system of linear Stratonovich Volterra integral equations reduce to system of linear algebraic equations which can be solved by a convenient numerical method. Also, the error analysis is proved under several mild conditions. We show the rate of convergence is O(h). Finally, by applying this method on two examples, we demonstrate accuracy and efficiency of the proposed method. All of the numerical calculation are performed on computer using a program written in MATLAB. (C) 2017 Elsevier B.V. All rights reserved.
暂无评论