共查询到20条相似文献，搜索用时 31 毫秒
1.
A set of the block pulse functions is applied to solve the Fredholm's and the Volterra's integral equations of the second kind. An algebraic equation in matrix form which is equivalent to the solution of the integral equation is developed. The approximate results are easily obtained by a few computations. An accurate solution canbe evaluated in a digital computer by solving the algebraic equation. Two examples are given. 相似文献
2.
Operational matrix based set-membership method for fractional order systems parameter identification
《Journal of The Franklin Institute》2021,358(18):10141-10164
In this paper, a new method is proposed to identify the coefficients and differentiation orders of fractional order systems with measurement noise. The proposed method combines the operational matrix method and the set-membership method. First, the block pulse functions operational matrix of the fractional differentiation is used to convert the fractional order system to an algebraic system. Then, the coefficients and differentiation orders are simultaneously estimated through a nest loop optimization process, where the optimal bounding ellipsoid set-membership algorithm is utilized to estimate the system’s coefficients and the orders are estimated with the interior-point method. The proposed method can accurately estimate the coefficients and differentiation orders of fractional order systems under any bounded measurement noise with less computational effort. Experimental results demonstrate the effectiveness of the proposed method. 相似文献
3.
Mohammad Hossein Heydari 《Journal of The Franklin Institute》2018,355(12):4970-4995
In this paper, a new direct method based on the Chebyshev cardinal functions is proposed to solve a class of variable-order fractional optimal control problems (V-OFOCPs). To this end, a new operational matrix (OM) of variable-order (V-O) fractional derivative in the Caputo sense is derived for these basis functions and is used to obtain an approximate solution for the problem under study. In the proposed method, the state and the control variables are expanded in terms of the Chebyshev cardinal functions with unknown coefficients, at first. Then, the OM of V-O fractional derivative and some properties of the Chebyshev cardinal functions are employed to achieve a nonlinear algebraic equation corresponding to the performance index and a nonlinear system of algebraic equations corresponding to the dynamical system in terms of the unknown coefficients. Finally, the method of constrained extremum is applied, which consists of adjoining the constraint equations derived from the given dynamical system and the initial conditions to the performance index by a set of undetermined Lagrange multipliers. As a result, the necessary conditions of optimality are derived as a system of algebraic equations in the unknown coefficients of the state variable, control variable, and Lagrange multipliers. Furthermore, some numerical examples of different types are demonstrated with their approximate solutions for confirming the high accuracy and applicability of the proposed method. 相似文献
4.
Wang Chi-Hsu 《Journal of The Franklin Institute》1983,315(2):91-102
A more rigorous derivation for the generalized block pulse operational matrices is proposed in this paper. The Riemann-Liouville fractional integral for repeated fractional (and operational) integration is integrated exactly, then expanded in block pulse functions to yield the generalized block pulse operational matrices. The generalized block pulse operational matrices perform as s-α(α\s>;0,α∈R) in the Laplace domain and as fractional (and operational) integrators in the time domain. Also, the generalized block pulse operational matrices of differentiation which correspond to sα(α\s>;0,α∈R) in the Laplace domain are derived. Based on these results, the inversions of rational and irrational transfer functions are proposed in a simple, accurate and efficient way. 相似文献
5.
S.G. Tzafestas 《Journal of The Franklin Institute》1980,309(6):399-438
In this paper a variety of optimal control (OC) problems for distributed- parameter (DP) systems are approached using mathematical programming (MP). First, the principal DP models in current use are given, a variety of DP objective functions is provided, and the OC problems based on them are formulated. Second, these models and objective functions are converted in algebraic form, as required by MP, and the solution procedure of the OC problems via MP is outlined. Third, a representative set of nonlinear programming results applied to DP systems is presented, and finally, a numvber of application examples is given. 相似文献
6.
Optimal parametrization in numerical construction of curve 总被引：1，自引：0，他引：1
E.B. Kuznetsov 《Journal of The Franklin Institute》2007,344(5):658-671
The application of the optimal parametric continuation method to constructing a solution set curve for a system of nonlinear algebraic or transcendental equations depending on a parameter is considered. There are discussed two approaches to solving this problem—the use of iterative methods and reduction to an initial value problem for a system of ordinary differential equations. The algorithm suggested in this paper can also be used for finding an appropriate initial approximation when solving a system of nonlinear algebraic or transcendental equations not depending on a parameter by an iterative method. 相似文献
7.
《Journal of The Franklin Institute》2019,356(16):9881-9906
This paper is concerned with robust stability analysis of second-order linear time-varying (SLTV) systems with time-varying uncertainties (perturbations). With the specific Lyapunov functions, a simple and neat algebraic criterion for testing uniformly asymptotic stability of SLTV systems are derived. Without transformation to a system of first-order equations, the new conditions are imposed directly on the time-varying coefficient matrices of the system. The main feature of the proposed algebraic criterion is that the uncertain coefficient matrices are time-varying and not necessarily symmetric. Finally, the proposed stability conditions are used to design the extending space structures system of the spacecraft. Simulation results are provided to illustrate the convenience and effectiveness of the proposed method. 相似文献
8.
H.R. Marzban 《Journal of The Franklin Institute》2004,341(3):279-293
A method for finding the optimal control of a linear time varying delay system with quadratic performance index is discussed. The properties of the hybrid functions which consists of block-pulse functions plus Legendre polynomials are presented. The operational matrices of integration, delay and product are utilized to reduce the solution of optimal control to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. 相似文献
9.
The main contribution of this paper is to develop an adaptive output-feedback control approach for a class of uncertain nonlinear systems with unknown time-varying delays in the pure-feedback form. Both the non-affine nonlinear functions and the unknown time-varying delayed functions related to all state variables are considered. These conditions make the controller design difficult and challenging because the output-feedback controller should be designed using only the output information. In order to overcome these conditions, we design an observer-based adaptive dynamic surface controller where the time-delay effects are compensated by using appropriate Lyapunov–Krasovskii functionals and the function approximation technique using neural networks. A first-order filter is added to the control input to avoid the algebraic loop problem caused by the non-affine structure. It is proved that all the signals in the closed-loop system are semi-globally uniformly bounded and the tracking error converges to an adjustable neighborhood of the origin. 相似文献
10.
研究了一种扩谱载波数字脉冲间隔调制SSC—DPIM(Spread spectrum carrier digital pulse interval modulation)技术并用于电力线载波扩谱通信系统．采用线性扫频SSC扩谱载波对DPIM符号进行编码，引入脉冲前导码作为传输数据块的同步信号以防止差错传播．介绍了数据传输速率及数据块传送差错率的理论分析结果．并采用单片机实现了SSC-DPIM电力线载波通信系统．实验结果表明，在同样的电力线网络环境下，其通信效果明显优于已有的电力线载波通信系统。 相似文献
11.
12.
R.V. Patel 《Journal of The Franklin Institute》1984,318(2):123-141
This paper describes a computational method for solving the problem of eigenvalue assignment in a multi-input linear system. The given system is first reduced to an upper block Hessenberg form by means of orthogonal state coordinate transformations. It is then shown how a sequence of state feedback matrices and orthogonal state coordinate transformations can be applied to obtain a block triangular structure for the resulting state matrix, where the matrices on the diagonal are square matrices in upper Hessenberg form and of dimensions equal to the controllability indices of the multi-input system. Furthermore, the structure of the corresponding input matrix is such that the problem of eigenvalue assignment in the multi-input system can be reduced to several single-input eigenvalue assignment problems where the dimensions of the single-input systems are equal to the controllability indices of the multi-input system. 相似文献
13.
研究了几种著名的分组密码体制的Ｓ盒所满足的代数方程的个数,如DES、AES、MARS、SERPENT等,分别计算出这几种分组密码的Ｓ盒从低次到高次的代数方程的个数,并把 计算结果和理论极小值进行了比较．此外,还针对一类对密码分析具有特别意义的不完全代数方程研究了Ｓ盒所满足的这类不完全代数方程的个数,通过这类方程的个数,可以看到它们的Ｓ盒与随机Ｓ盒的差别． 相似文献
14.
一类Bent函数的构造 总被引：5，自引：0，他引：5
给出了具有任意偶数个变元的Bent函数的一种构造办法.该方法通过级联二个半Bent函数得到Bent函数,所构造的Bent函数具有极大的代数次数和可控的单项式项数。 相似文献
15.
Boolean control networks are a kind of discrete logical dynamical systems. They are recently attracting considerable interest as computational models for genetic and cellular networks. In this paper, we investigate the cascading state-space decomposition problem for Boolean control networks by nested method. Firstly, based on the semi-tensor product of matrices, we obtain some algebraic conditions for the cascading state-space decomposition. Secondly, the multi-layer nested block matrix is defined, and two necessary and sufficient conditions are put forward based on this kind of matrices. Besides, a method is given to design controllers. Finally, an example is given to display the effectiveness of the method provided in this paper. 相似文献
16.
This paper investigates the problem of global stabilization of switched nonlinear systems in non-triangular form whose subsystems are not assumed to be asymptotically stabilizable. The use of multiple Lyapunov functions (MLFs) method permits removal of a common restriction in which the nonlinear structures in the non-switched nonlinear systems are restricted to a triangular structure when applying backstepping. Using the MLFs method and the adding a power integrator technique, we design state-feedback controllers for individual subsystems and construct a switching law to guarantee asymptotic stability of the closed-loop switched system. As an application of the proposed design method, the global stabilization problem of a continuously stirred tank reactor (CSTR) system and two inverted pendulums which cannot be handled by the existing methods is investigated. 相似文献
17.
M.H. Heydari 《Journal of The Franklin Institute》2019,356(15):8216-8236
The main goal of this study is to develop an efficient matrix approach for a new class of nonlinear 2D optimal control problems (OCPs) affected by variable-order fractional dynamical systems. The offered approach is established upon the shifted Chebyshev polynomials (SCPs) and their operational matrices. Through the way, a new operational matrix (OM) of variable-order fractional derivative is derived for the mentioned polynomials.The necessary optimality conditions are reduced to algebraic systems of equations by using the SCPs expansions of the state and control variables, and applying the method of constrained extrema. More precisely, the state and control variables are expanded in components of the SCPs with undetermined coefficients. Then these expansions are substituted in the cost functional and the 2D Gauss-Legendre quadrature rule is utilized to compute the double integral and consequently achieve a nonlinear algebraic equation.After that, the generated OM is employed to extract some algebraic equations from the approximated fractional dynamical system. Finally, the procedure of the constrained extremum is used by coupling the algebraic constraints yielded from the dynamical system and the initial and boundary conditions with the algebraic equation extracted from the cost functional by a set of unknown Lagrange multipliers. The method is established for three various types of boundary conditions.The precision of the proposed approach is examined through various types of test examples.Numerical simulations confirm the suggested approach is very accurate to provide satisfactory results. 相似文献
18.
Ignacy Duleba Wissem Khefifi Iwona Karcz-Duleba 《Journal of The Franklin Institute》2012,349(1):201-215
In this paper a layer, Lie algebraic method of motion planning for nonholonomic systems is presented. It plans locally a motion towards a goal by searching for optimal directions in equi-cost spaces. The spaces are easy to determine via exploiting Lie algebraic properties of vector fields that define the controlled system. The method was illustrated on the unicycle robot and the inverted pendulum. 相似文献
19.
Our paper deals with an effective application of the pseudospectral method to solution of Hamiltonian boundary value problems in optimal control theory. The developed numerical methodology is based on the celebrated Gauss pseudospectral approach. The last one makes it possible to reduce the conventional Hamiltonian boundary value problem to an auxiliary algebraic system. The implementable algorithm we propose is computationally consistent and moreover, involves numerically tractable results for a relative small discretization grids. However, the solution of the obtained algebraic equations system may has a low convergence radius. We next use the differential continuation approach in order to weaken the necessity of the well-defined initial conditions for the above algebraic system. The presented solution procedure can be extremely useful when the generic shooting-type methods fail because of sensitivity or stiffness. We discuss some numerical results and establish the efficiency of the proposed methodology. 相似文献
20.
The present paper proposes a numerical approach to a linear optimal control problem with a quadratic performance index. In this technique, the time interval is divided into a number of time segments and all of the unknown functions which appear in the performance index are either interpolated linearly with respect to time or assumed to be constant in each time segment. The augmented performance index is discretized within each time element through the ordinary finite element technique.The main advantage of the present method is as follows: all of the necessary conditions for the performance index to be stationary can be expressed in the form of algebraic equations and the performance sequence of the state variables can be eliminated. As a result, the optimal control problem is reduced to the simple one of finding the sequence of control variables alone, which minimizes the quadratic performance index.A general formulation of the method is given and simple numerical examples are shown to demonstrate the effectiveness of the technique. 相似文献