Yen-Ping Shih

Parameter identification via Laguerre polynomials

An operational matrix for the integration of the Laguerre vector whose elements are the Laguerre polynomials is introduced and applied to parameter identification of time invariant linear systems. Due to the unique property of the operational matrix, the algorithms to formulate the algebraic equations to estimate unknown parameters are recursive and suitable for computer programming. Examples with satisfactory results are given.

Analysis and optimal control of time-varying linear systems via Walsh functions

Abstract Extension of Walsh functions to the analysis of time-varying linear systems is made by the introduction of the product matrix of Walsh vector and its transpose, and the operational property of product matrix. The operational matrix for the backward integration of Walsh functions is first introduced. Therefore, the state transition matrix of optimal control of linear time-varying systems with quadratic performance index can be integrated approximately using Walsh functions. The solution of the state transition matrix leads to piecewise constant gains equally distributed.

Laguerre operational matrices for fractional calculus and applications

The Laguerre operational matrices for the integration and differentiation of a Laguerre vector whose elements are Laguerre polynomials are generalized to fractional calculus for investigating distributed systems. The generalized operational matrices corresponding to 8, 1/8, 8/√(82+1) and exp (−8/(8+1)) are derived as examples. Comparison of the Laguerre series approximate inversions of irrational Laplace transforms with exact solutions is very satisfactory.

Analysis and optimal control of time-varying systems via Chebyshev polynomials

Abstract The operational properties of the forward and backward integration and the product of Chebyshev polynomials are derived. These properties are applied to the analysis and optimal control of time-varying linear systems by the approximation of time functions by truncated Chebyshev series. Due to the unique property of the Chebyshev polynomials excellent results are obtained as demonstrated by examples.

Laguerre series solution of a functional differential equation

This paper presents a Laguerre series method for the solution of a functional differential equation of the type (d/dt)y(t) = Ay(λt) + By(t), with given initial conditions. The method consists of the following steps : (1) represent y(t) and y(λt), respectively, by series of the Laguerre polynomials gi(t) and gi(λt) ; (2) expand gi(λt) into Laguerre series of gi(t) ; (3) integrate the Laguerre series approximation of the functional differential equation by an operational matrix approach. Two numerical examples are given with satisfactory results.

Simplification of z -transfer functions by continued fractions †

A computer-oriented procedure for the simplification of a z -transfer function is presented. The method consists of (1) transformation of the z-transfer function into the w domain by the bilinear transformation, w=(z− l)/)z+ 1), (2) continued fraction expansion of the w -transfer function into the Cauer second form, (3) keeping the first several quotients and discarding others, (4) converting the truncated continued fraction into z-transfer function of low order. An example is used to illustrate the rapid rate of convergence.

A combined approach to fuzzy model identification

A combined approach for discrete-time fuzzy model identification is proposed. By this approach, the identification is performed in two stages. First, the linguistic approach is utilized to obtain an approximate fuzzy relation from the sampled nonfuzzy input-output data. This approximate fuzzy relation is then used as the initial estimate for the second stage in which a more accurate fuzzy relation is determined by the approach of numerical resolution of fuzzy relational equation. A recursive identification algorithm based on the prediction-error method is derived for optimally resolving the numerical fuzzy relational equation by minimizing a quadratic performance index. This algorithm makes the proposed approach particularly attractive to online applications. Two numerical examples are provided to show the superiority of the combined approach over other methods. >

Parameter Estimation of Bilinear Systems Via Walsh Functions

Abstract Walsh product matrix is formed by the multiplication of Walsh vector and its transpose. The operation of Walsh product matrix on a coefficient vector equals the product of a coefficient matrix and a Walsh vector. This unique property of Walsh function is used to determine the unknown parameters of a general bilinear system from the input-output data. An example with satisfactory result is given.

Analytical solutions for freezing a saturated liquid inside or outside cylinders

Abstract By the use of an analytical iteration technique successive solutions for the instantaneous frozen layer thickness and temperature profile for the freezing of a saturated liquid inside cylindrical containers with constant heat transfer coefficient are generated. Comparison of the results with experimental data and numerical solutions shows satisfactory coincidence. Successive solutions for freezing of a saturated liquid outside cylinders are also derived and compared with numerical solutions.

Explicit solutions of integral equations via block pulse functions

A new method to obtain the explicit solutions of integral equations via block pulse functions is proposed. The elegant Laplace transform technique is used to integrate the block pulse convolution matrix in terms of the block pulse functions. Based on these results, the solutions of integral equations can be recursively calculated. The first and second order integral equations of the first kind, and the integral equations of the second kind arc all solved via this new approach.