摘要:

This paper discusses a summary derivation of maximum aposterioriestimation for continuous and discrete non-linear systems. It is known that with Gaussian aprioristatistics, the maximum aposterioriestimate is equivalent to an appropriate least squares fit. Filtering, fixed interval and fixed point smoothing algorithms for approximate non-linear estimation are obtained for the least squares eurve fit using ‘ running time ’ and ‘ fixed time ’ invariant embedding. Examples illustrating the use of the algorithms are presented.

ISSN:0020-7179    

DOI:10.1080/00207177008905876

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

A theorem on the stability analysis of a system of n differential equations of the first order is based on the relations between the state space X and the velocity space Ẋ. Two numerical examples illustrate the implications of the theorem in two and three-dimensional spaces.

ISSN:0020-7179    

DOI:10.1080/00207177008905877

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

A sufficient condition is presented for a simple problem in the calculus of variations. This condition is derived by comparing the functional to be minimized to another functional such that a zero of this is a minimizing element of the former functional. The procedure which results from the sufficient condition to solve the variational problem is specially suited for integrands which do not have some partial derivatives at some points of their domain of definition. Several examples are given which illustrate the range of applicability of the method.

ISSN:0020-7179    

DOI:10.1080/00207177008905878

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The Rita method is used to develop general approximate solutions to second-order non-linear differential-difference equations subjected to a sinusoidal driving function. Stability criteria are stated and resonance properties are studied. A number of examples are considered, and the results are compared to analogue computer simulations of the equations.

ISSN:0020-7179    

DOI:10.1080/00207177008905879

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The estimation of weighting sequence descriptions for processes, using a pseudo-random test signal and correlation analysis, is studied using a matrix approach and standard discrete least-square methods. This clarifies a number of points arising in practical application.

ISSN:0020-7179    

DOI:10.1080/00207177008905880

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The estimation of weighting sequence description of processes where autocorrelated noise corrupts the output is studied, and the qualitative improvement obtained by using generalized least–square techniques shown. These are confirmed by computer simulated experiments.

ISSN:0020-7179    

DOI:10.1080/00207177008905881

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The problem of decoupling and inverting dynamic systems is considered. Attention is focused on the problems that arise as available linear techniques ore applied to nonlinear systems. The decoupling of non-linear multi-variate differential equations is illustrated in a series of three examples.

ISSN:0020-7179    

DOI:10.1080/00207177008905882

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

Sufficient conditions for the existence of periodic motion of linear time-invariant systems when represented in phase variable form are obtained through Liapunov's second method. A method of constructing Liapunov functions to obtain conditions for non-asymptotic, non-periodic stability of these systems is suggested. Matrix analogues of these conditions serve to determine the orbital motion and non-asymptotic non-periodic stability of coupled systems whose matrix coefficients are simultaneously diagonalizable.

ISSN:0020-7179    

DOI:10.1080/00207177008905883

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The desired transfer function is expanded into factors having quadratic denominators. Each factor is identified with the setA, B, C, Dof matrices of the state-space representation of a capacitively terminated two-port network that is specified by a transmission matrixT. An equivalence is obtained between the required stateAmatrix and the correspondingTmatrix. Then,Tmatrix synthesis techniques that were developed specifically for use with differential operational amplifiers are applied to obtain realizations of theAmatrix. By synthesizing different decompositions of theTmatrix, different equivalent realizations are obtained and the problem of determining appropriate input and output access ports corresponding to theB, CandDstate matrices is facilitated. A practical feature of the method is that all of the basic transfer functions can be realized with grounded amplifiers and capacitors.

ISSN:0020-7179    

DOI:10.1080/00207177008905884

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

A method is presented for determining approximate solutions to a class of differential equations characterized by:where resonance phenomena (arising, for example, when ƒ(x,ẋ,t) = x cosω0t) may be neglected. The approximation is developed from an asymptotic expansion in terms of the amplitude and phase of the solution. Three examples are considered in illustration of the application of the approximation technique, and using an integral error function, solution error is shown graphically for these examples in terms of equation parameters. An expression for the approximate solution is derived which makes it possible to determine solution accuracy for any functionf(x,x˙,t) once the approximate amplitude envelope and phase relationships have been derived. Graphical solutions demonstrate the accuracy which can be maintained even up to relatively large values of the parameter µ.

ISSN:0020-7179    

DOI:10.1080/00207177008905885

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor