摘要:

Ljung and Caines[1,2 and 4], establish almost sure convergence and asymptotic normality of prediction error estimators for approximately identifying a given dynamical system as an element within a postulated class of models which need not necessarily include the sytem. These theorems amy be regarded as instances of a strong law of large numbers and a central limit theorem. This note complements the results of Ljung and Caines by establishing a Donsker functional central limit theorem, classical law of the iterated logarithm and Strassen functional law of the iterated logarithm for prediction error estimators These results may be used to find almost sure rates of convergence as well as limiting distributions of various functionals of the sequence of estimators

ISSN:0090-9491    

DOI:10.1080/17442508808833507

出版商:Gordon and Breach Science Publishers, Inc    

年代:1988

数据来源: Taylor

摘要:

An adaptive control problem for linear, continuous time, discrete delay stochastic systems is described and solved in this paper. A solution of the adaptive control problem means that the family of maximum likelihood estimators are shown to be strongly consistent and te average costs are shown to converge to the optimal average cost. The unknown parameters in the model appear affinely in the drift term of the stochastic differential equation. The assumptions that are made for the solution are natural and verifiable

ISSN:0090-9491    

DOI:10.1080/17442508808833508

出版商:Gordon and Breach Science Publishers, Inc    

年代:1988

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508808833506

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor