摘要:

The stability of a class of continuouous systems with non-stationary random coefficients is studied. It is shown that the trivial equilibrium solution is moan-square asymptotic stable as long as the expected values of the absolute value of the random coefficients are integrable. Several examples are considered and discussed.

ISSN:0020-7721    

DOI:10.1080/00207727708942115

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A stochastic approximation technique has been developed for optimal state estimation in a class of systems modelled by the generalized Itô-Doob non-linear stochastic integral equation, the observation process is assumed to be available as a non-linear transformation of the state process with additive measurement errors. The theory of martingales in general, and the innovations approach in particular, have boon employed to yield conceptually simpler solution models with explicit expressions for operational implementation. Stochastic approximation techniques are utilized for numerical computation of innovations processes, and consequently the system state of non-linear dynamical systems. A comparative study of the computational results demonstrates the fact that stochastic approximation may turn out to be superior to other existing methods, in particular, the extended Kalman technique and the invariant imbedding approach, for certain optimal estimation problems. Having observed that the principal obstacle in implementation of the filter algorithm for non-linear systems rests in computation of the associated gain function, an adaptive scheme for improvement has been proposed, based on the innovations property of the filter. Some problems resulting from this study have also been mentioned for further investigation. It is envisaged that the algorithm will find application in some problems in engineering and also yield more compact bases for optimal design and control of other complex phenomena.

ISSN:0020-7721    

DOI:10.1080/00207727708942116

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Comprehensive study of many complex phenomena of biological and physiological systems should essentially be based on stochastic postulates. Having emphasized this feature, this paper develops a non-linear stochastic model encompassed by the generalized Itô-Doob equations, with particular reference to optimal estimation of causative factors and therapy for cancer. Concise mathematical algorithms yielding conceptually simpler and explicit solution schemes, based on the innovations concept and theory of martingales, have been derived. The possibility that this algorithm, using appropriate experimental observations, may provide compact and precise mathematico-biophysical representations for analysis and control in other physiological problems, has also been indicated.

ISSN:0020-7721    

DOI:10.1080/00207727708942117

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Weak convergence results are obtained for a sequential regression algorithm that arises in the identification of nonlinear, memoryless systems and the adaptive design of moving average filters. The algorithm is shown to be weakly consistent if the system input is a wide-sense stationary sequence of order four that satisfies certain covariance and fourth-cumulant conditions. The conditions are essentially asymptotic independence requirements that permit one to relax the (usually required) strict independence requirements on the input data.

ISSN:0020-7721    

DOI:10.1080/00207727708942118

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

In this paper the Brunovsky control canonical form (Brunovsky 1966) is used to synthesize control policies for the linearized ‘ industrial dynamics ’ model presented by Bradshaw and Daintith (1977). It is shown by the presentation of the results of computer simulation studies that the use of such control policies results in superior transient behaviour even when the closed-loop eigenvalues are the same.

ISSN:0020-7721    

DOI:10.1080/00207727708942119

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Linearized decision rules in the aggregate production scheduling framework are compared through simulation experiments to see if decisions are improved when adaptive feedback elements are built into the rule. Our results, based on some non-parametric tests, show the need for determining an optimal trade-off between stabilization and experimentation through a specified cost functional.

ISSN:0020-7721    

DOI:10.1080/00207727708942120

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Boundary-value problems that arise in practice often exhibit rapid growth and decline behaviour. The single interval discrete weighted residual method (Nouman and Schonbach 1977) approach may be inadequate for solving such boundary-value problems. This paper, therefore, is devoted to developing and illustratingmulti-intervaldiscrete weighted residual methods (DWRM's) for solving these numerically sensitive problems. The numerical difficulties associated with solving these boundary-value problems are reduced by dividing the problem interval into a number of sub-intervals and constructing the DWBM solution piecewise in each of these subintervals. Joining conditions are imposed at the interfaces of adjacent subintervals to piece together the individual solutions in each of the subintervals. The modal coefficients are evaluated as the solution of the combined DWRM and joining condition equations. Multi-interval DWRM's provide computationally efficient procedures for solving numerically sensitive boundary-value problems. This multi-interval viewpoint can also be applied to improve the numerical accuracy of other boundary-value problem solution techniques.

ISSN:0020-7721    

DOI:10.1080/00207727708942121

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

This note is to examine the approximation problems of systems with infinite-dimensional state space. The well-known Padé formula and Khovanskii's generalized Padé formula are extended to the time-domain. Approximate finite-dimensional state models are established for typical elements with infinite-dimensional state-space.

ISSN:0020-7721    

DOI:10.1080/00207727708942122

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Using our recently developed theory of duality for convex integral functionals, dual problems are constructed for linear functional programming andLpprogramming.

ISSN:0020-7721    

DOI:10.1080/00207727708942123

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor