This paper analyzes the application of Laguerre polynomial expansion to linear systems. It can be applied to the solution of linear state equations by using an algebraic matrix to determine the coefficients of the Laguerre expansion. It also can be applied to system identification by using the expansion to determine the coefficients in the transfer function. Examples are given to demonstrate the accuracy of finite order expansion by Laguerre polynomials. 相似文献
Synchronous data transmission systems that transmit information over dispersive channels often employ adaptive equalization techniques in the processing of the received signals. Most equalizers presently used in communication systems are of the tapped delay line (TDL) type. In this paper, we propose a class of adaptive equalizers of which the TDL equalizer is a member. Another interesting member of this class is the Laguerre adaptive equalizer which is to be introduced in this paper. The configuration of the Laguerre equalizer is developed. It is found, as shown by the examples, that the Laguerre equalizer is more accurate, and is less sensitive to timing error than the conventional TDL equalizer. 相似文献
For the approximation of real functions in L2(0, ∞) that are frequently encountered in signal analysis and parameter identification, analytical and computer studies suggest the use of Laguerre functions. Such functions can form at least locally optimal or near-optimal sets. The results are shown for continuous systems to be encouragingly flat, indicating low sensitivity to the position of the Laguerre multiple pole. Relationships to linear time-invariant discrete systems are given, using discrete Laguerre functions. 相似文献
This paper analyses the linear time-varying system by the shifted Legendre polynomials expansion. Using the operational matrix for integrating the shifted Legendre polynomials, the dynamic equation of a linear time-varying system is reduced to a set of simultaneous linear algebraic equations. The coefficients of the shifted Legendre polynomials expansion can be determined by using the least-squares method. An example is given to demonstrate the accuracy of shifted Legendre polynomials expansion of finite terms and it is compared with the results of the Laguerre method. 相似文献
The problems of identification, analysis and optimal control have been recently studied via orthogonal functions. The particular orthogonal functions used up to now are the Walsh, the block-pulse and the Laguerre functions. In this paper, the Chebyshev functions are introduced and solutions for the aforementioned problems are established. The algorithms proposed are analogous to those already derived for the Walsh, block-pulse and Laguerre functions. The Chebyshev series approach presented here appears to have certain advantages over other orthogonal series, and they may therefore be more suitable for the study of the problems of identification, analysis and optimal control. 相似文献
This paper is devoted to the issue of a robust predictive control for linear discrete-time systems by using Meixner-like model. The Meixner-like functions are an extension of Laguerre functions and convenient when the system has a slow start or delay. To ensure the reduction of the parameter number in the Meixner-like model, the optimization of parameters characterizing the Meixner-like functions is proposed. This proposed robust predictive control copes with physical constraints and geometrical constraints due to parameter uncertainties, which are estimated by using the Unknown But Bounded Error (UBBE) approach, and leads to the min-max optimization problem. 相似文献
A new time-domain approach to the derivation of a Chebyshev scale matrix is presented. The derived Chebyshev scale matrix, together with the Chebyshev integration matrix, is used to analyze differential equations containing terms with a scaled argument. The results are expressed in terms of Chebyshev series. As illustrated in the included examples, the Chebyshev series solution converges faster than that represented in Laguerre series. 相似文献
For the following mixed bivariate probability distribution between a discrete random variable X and a continuous random variable Λ: where α, β > 0, 0 < p = 1 ? q < 1, x=0,1,2,...,a canonical expansion is obtained in terms of the Laguerre and Meixner orthogonal polynomials. The chance mechanisms giving rise to this mixed bivariate distribution are also discussed. 相似文献
This paper gives a general review of the Theory of Nonlinear Systems. In 1960, the author presented a paper “Theory of Nonlinear Control” at the First IFAC Congress at Moscow. Professor Norbert Wiener, who attended this Congress, drew attention to his work on the synthesis and analysis of nonlinear systems in terms of Hermitian polynomials in the Laguerre coefficients of the past of the input.Wiener's original idea was to use white noise as a probe on any nonlinear system. Applying this input to a Laguerre network gives u1, u2,…, us, and then to a Hermite polynomial generator gives V(α)'s. Applying the same input to the actual nonlinear system gives output c(t). Putting c(t) and V(α)'s through a product averaging device, we get , where the upper bar denotes time average and Aα's can be considered as characteristic coefficients of the nonlinear system. A desired output z(itt) may replace c(itt) to get a new set of Aα's.The Volterra functional method suggested by Wiener in 1942 has been greatlydeveloped from 1955 to the present. The method involves a multi-dimensional convolution integral with multi- dimensional kernels. The associated multi-dimensional transforms are given by Y.H. Ku and A.A. Wolf (J. Franklin Inst., Vol. 281, pp. 9–26, 1966). Wiener extended the Volterra functionals by forming an orthogonal set of functionals known as G-functionals, using Gaussian white noise as input. Volterra kernels and Wiener kernels can be correlated and form the characteristic functions of nonlinear systems.From an extension of the linear system to the nonlinear system, the input-output crosscorrelation φxy can be shown to be equal to the convolution of system impulse response h1 with the autocorrelation φxx. Using the white noise as input, where its power density spectrum is a constant, say, A, the crosscorrelation is given by φxy(σ) = Ah1(σ), while the autocorrelation is φxx(τ) = Au(τ). This extension forms the basis of an optimum method for nonlinear system identification. Measurement of kernels can be made through proper circuitry.Parallel to the Volterra series and the Wiener series, another series based on Taylor-Cauchy transforms developed since 1959 are given for comparison. The Taylor-Cauchy transform method can be applied in the analysis of simultaneous nonlinear systems. It is noted that the Volterra functional method and the Taylor-Cauchy transform method give identical final results.A selected Bibliography is appended not only to include other aspects of nonlinear system theory but also to show the wide application of nonlinear system characterization and identification to problems in biology, ecology, physiology, cybernetics, control theory, socio- economic systems, etc. 相似文献
Currently a wide range of information system development methods exists, each method supporting different sets of concepts and being supported by different techniques and tools. For many large and complex systems a multi-method approach would be preferable but the fragmentation of contemporary methods does not cater at present for a unified representation of system specifications. The AMADEUS project attempts to redress this situation by enabling the integration of different contemporary development methods at the semantic level. This paper addresses the problems involved in the current multiplicity of development methods and proposes a means of enabling system developers to view information system development in a unified way. 相似文献
