摘要:

A new ‘cone ratio’ data envelopment analysis (DEA) model that substantially generalizes the Charnes-Cooper-Rhodes (CCR) model and the Charnes-Cooper-Thrall approach characterizing its efficiency classes is developed and studied. It allows for infinitely many decision-making units (DM Us) and arbitrary closed convex cones for the virtual multipliers as well as the cone of positivily of the vectors involved. Generalizations of linear programming and polar cone equalizations arc the analytical vehicles employed.

ISSN:0020-7721    

DOI:10.1080/00207728908910197

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The operational matrix or integration of a Jacobi vector whose elements are Jacobi polynomials is introduced and applied to solve variational problems by a direct method. Illustrative examples are given to demonstrate that only a small number of shifted-Jacobi polynomials are needed to obtain an accurate solution.

ISSN:0020-7721    

DOI:10.1080/00207728908910198

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A method for finding the inverse of Laplace transforms using polynomial series is discussed. It is known that any polynomial series basis vector can be transformed into Taylor polynomials by use of a suitable transformation. In this paper, the cross product of a polynomial series basis vector is derived in terms of Taylor polynomials, and as a result the inverse of the Laplace transform is obtained, using the most commonly used polynomial series such as Legendre, Chebyshev, and Laguerre. Properties of Taylor series are first briefly presented and the required function is given as a Taylor series with unknown coefficients. Each Laplace transform is converted into a set of simultaneous linear algebraic equations that can be solved to evaluate Taylor series coefficients. The inverse Laplace transform using other polynomial series is then obtained by transforming the properties of the Taylor series to other polynomial series. The method is simple and convenient for digital computation. Illustrative examples are also given,

ISSN:0020-7721    

DOI:10.1080/00207728908910199

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A method for finding the optimal control of linear distributed-parameter systems using polynomial series is discussed. It is known that any polynomial series basis vector can be transformed into a Taylor polynomial by the use of a suitable transformation. In this paper, the optimal control of a distributed-parameter system is simplified into the solution of a linear two-point boundary value problem, and, as a result, the optimal control is obtained via a Taylor series. It is shown that the implementation of Taylor series for this problem involves the use of an ill-conditioned matrix commonly known as the Hilbert matrix. The optimal control of linear distributed-parameter systems using other polynomial series is then calculated by transforming the properties of the Taylor series into other polynomial series. The formulation is straightforward and convenient for digital computation. An illustrative example is given.

ISSN:0020-7721    

DOI:10.1080/00207728908910200

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The analysis of linear optimal control systems incorporating observers via single-term Walsh series is considered and very simple algorithms convenient for computations are presented. Compared with the previous methods using Walsh functions (WF), block-pulse functions (BPF), shifted Chebyshev series, the results are simpler in form. An example is presented to illustrate the use of the method.

ISSN:0020-7721    

DOI:10.1080/00207728908910201

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A new technique for the detection and height estimation of buried metallic objects is developed. This technique is bused on the phase characteristics of both transmitted and received signals. A discrete Fourier transform via a fast Fourier transform algorithm is used to compute the phase characteristic. The height of the buried metallic object is estimated by detecting the transition frequency and measuring the phase difference between the transition frequency and the next frequency component in the spectrum of the received signal. Computer simulation studies show that this technique is efficient, reliable, and provides sufficient accuracy.

ISSN:0020-7721    

DOI:10.1080/00207728908910202

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A general basis for using orthogonal functions to approximate the variables of a dynamic output feedback control system is presented. The use of an operational matrix of integration reduces the problem to a set of linear algebraic equations. The result is also useful for implementing open-loop approximation of derived closed-loop control. The flexible controller structure provides easy adaptation to feedback configurations using state, output, dynamic output or observer output, and feedback compensator. As an example, an approximation analysis of dynamic output feedback control via Fourier series is investigated.

ISSN:0020-7721    

DOI:10.1080/00207728908910203

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A reduced-order filler algorithm is developed for estimation of the complementary states of a linear system driven by white noise. The estimator gives an unbiased estimate of the states, and the error in the estimate is orthogonal to the subspace of the observations of those states that are common to the observations and the estimated states, The filter performance is suboptimal relative to the full-order optimal linear filter, but benefits are reaped from computational savings in the filtering and associated Riccati equations. The algorithms are developed using a concept of the ‘reduced-order innovation process’. The design uses only a priori information for z, the states to be estimated. The estimator is shown to be unique. The requirements of the stability of the filter are also presented, and its determination can precede its implementation. The basic limitation of this approach is that one is constrained by the minimum order of the filter, because of the assumption in (2.11) that the states to be estimated are complementary to the observed states.

ISSN:0020-7721    

DOI:10.1080/00207728908910204

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A reduced-order algorithm for the smoothing of the complementary states of a linear system is developed. If there are l complementary states to be estimated, the smoothing problem using the reduced-order algorithm involves solving a hamiltonian system of equations of order 2l as compared to an order of 2n for full-order smoothing. We also obtain realizations for fixed interval smoothing using a two-filter structure, fixed point, and fixed lag smoothing. Equivalent filtering and smoothing problems for the discrete case are also discussed. Finally, an example is presented to show that the reduced-order algorithms perform quite satisfactorily compared to the optimal full-order Kalman-type algorithms. Given the computational savings, reduced-order complementary estimators might prove to be useful in situations where computation and memory limitations are an important factor.

ISSN:0020-7721    

DOI:10.1080/00207728908910205

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Minimal state-space realizations for two special types of two-dimensional discrete systems are derived. These two special types depend on the transfer function (i) with separable denominator and (ii) with separable numerator. The method is conceptually and computationally simple.

ISSN:0020-7721    

DOI:10.1080/00207728908910206

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor