Double-shifted Chebyshev series for convolution integral and integral equations

Double-shifted Chebyshev polynomials are developed in this study to approximate the solutions of the convolution integral, Volterra integral equation, and Fredholm integral equation. This method simplifies the computations of integral equations to the successive solutions of a linear algebraic equation in matrix form. In addition, the computational complexity can be reduced remarkably. Three examples are illustrated. It is seen that the proposed approach is straightforward and convenient, and converges faster in finding approximations than other existing orthogonal function methods.     

Discrete pulse orthogonal functions for the analysis,parameter estimation and optimal control of linear time-varying digital systems

The analysis, parameter estimation and optimal control of linear time-varying digital systems are facilitated in this study. The discrete pulse orthogonal functions (DPOFs) and their operational matrices are taken as a sharp tool. The applications of DPOFs to digital control systems are analogous to those of the known block pulse functions (BPFs) in continuous systems. By applying the DPOFs, approximate solutions of digital time-varying systems can easily be obtained by convenient algorithms. Three examples are illustrated to demonstrate the proposed DPOF technique, and the approximate results are very accurate and satisfactory.     

Interface study for stainless steel fibre-reinforced aluminium matrix composite

Regular interface zones with uniform thickness in AISI 304 stainless steel-reinforced aluminium-matrix composite have been obtained using a vacuum high-pressure diffusion-bonding technique. Extensive and intensive experiments were performed to examine the growth of interfacial compounds with the variation of hot-pressing time and temperature. In the initial stage, the overall growth rate of the interface was found to follow a parabolic law. After a certain diffusion time, the interface growth rate fell behind that predicted by the parabolic law. A modified parabolic law has been established to explain the deviation and proved to be a better model to fit the experimental data. An activation energy of 152 kJ mol^-1 was found, which was somewhat lower than that obtained by previous work. The lower value of activation energy is attributed to the pressure (70 MPa) applied during hot pressing. Energy dispersive spectroscopic analysis and microhardness measurement indicated that the interface zone consists of a mixture of intermetallic compounds Fe(Cr, Ni)Al₂, Fe(Cr, Ni)Al₃ and (Fe, Cr, Ni)₂Al₇. This revised version was published online in November 2006 with corrections to the Cover Date.     

基于矩阵运算的超网络构建方法研究及特性分析

基于邻接矩阵Khatri-Rao积运算及Khatri-Rao和运算,研究了构建超网络的方法,并通过边际节点度及联合节点度来研究超网络的内在机理。将Khatri-Rao积运算迭代地应用于一个初始图序列组成超网络的邻接矩阵,得到一个分形维数不超过3的自相似超网络。若所有初始图均是连通非二分图,则得到的超网络同时具有小世界特性,其直径不超过所有初始图直径和的两倍。此外,将Khatri-Rao和运算顺次应用于多个初始图序列组成超网络的邻接矩阵,得到一个边际节点度呈一维高斯分布而联合节点度呈高维高斯分布的随机超网络。最后,给出了基于矩阵运算的超网络构建方法的若干性质。     

New approach to the optimal control of time-varying linear systems via Chebyshev series

The general expression of the shifted Chebyshev series approximation for any two arbitrary functions has been presented by Chou and Horng (1985 a). The expression is recursive and useful in time-varying and non-linear systems. Due to the property, the design of gains for the time-varying optimal control system with a quadratic performance measure is studied by directly solving the Riccati equation in this paper. The method considered is much simpler than other design techniques. An example is illustrated. Only a small number, m = 4, of Chebyshev series is needed to produce a satisfactory outcome.     

Algebraic method for the design of output deadbeat controller

Based on the deadbeat model approach and the technique of output spectra matching, an algebraic method for the design of an approximate deadbeat controller with a specified configuration has been proposed. The chosen controller is determined by solving a set of simultaneous algebraic equations. One example is given to show the characteristic features of this approach.     

Application of shifted Chebyshev series to the optimal control of linear distributed-parameter systems

By use of a particular property of the shifted Chebyshev series, the optimal control of a distributed-parameter system is simplified into the optimal control of a linear time-invariant lumped-parameter system. Next, a directly computational formulation for evaluating the optimal control and trajectory of a linear distributed-parameter system is developed. The formulation is straightforward, and convenient for digital computation. An illustrative example is given to demonstrate the applicability of the proposed method     

Analysis and identification of non-linear systems via shifted Jacobi series

Based on shifted Jacobi series, algorithms have been established for the analysis and identification of non-linear systems described by a Hammerstein model consisting of a single-valued non-linearity followed by a linear plant. Moreover, the parameter estimation of a certain non-linear lumped system is also presented. By using the shifted Jacobi expansion for the analysis, the solution of a non-linear state equation is reduced to the solution of a linear algebraic matrix equation. For the identification, by expanding the measured input-output data into the shifted Jacobi series the unknown parameters of the non-linear system are estimated through the least-squares method. Examples are given to demonstrate the usefulness of this approach.     

Synthesis of digital control systems using discrete Walsh polynomials

The use of discrete Walsh polynomials to synthesize a digital control system and determine suitable internal system structure from its prescribed external (input/output) behaviour is studied in this paper. Algorithms for the synthesis of discrete system transfer functions and state equations are presented. The discrete Walsh approach method transforms the original model difference equations into computationally convenient algebraic forms. Two examples in which a transfer function and a state equation are synthesized illustrate the discrete Walsh technique.     

Discrete Walsh operational matrices for analysis and optimal control of linear digital systems

By the introduction of the shift transformation matrix, direct product matrix and summation matrix of the discrete Walsh series, the analysis of time-varying digital control systems is facilitated and the approximate solution of time-invariant digital optimal control problems is achieved of this study. The design algorithms of digital optimal control are based on the discrete variational principle combined with the idea of penalty functions to obtain the conveniently computational formulations for evaluating the optimal control and trajectory. Three examples are illustrated by using the discrete Walsh approach.