Stochastic adaptive control and Martingale limit theory

Author

Solo, Victor

Author_Institution

Dept. of Electr. & Comput. Eng., Johns Hopkins Univ., Baltimore, MD, USA

Volume

35

Issue

1

fYear

1990

fDate

1/1/1990 12:00:00 AM

Firstpage

66

Lastpage

71

Abstract

Recently, S.P. Meyn and P.E. Caines (ibid., vol.AC-32, p.220-6, 1987) have used ergodic theory for Markov processes to give the first asymptotic stability analysis of a nontrivial stochastic adaptive control problem. By nontrivial is meant a stochastic adaptive control problem whose parameter variation has finite nonzero power. They correctly observed that the stochastic Lyapunov function methods fail here, because there is no almost sure parameter convergence. It is shown here how Martingale asymptotics can be used to produce many results close to those of Meyn and Caines, as well as to supply some new observations. Strengths and weaknesses of both approaches are discussed

Keywords

Markov processes; adaptive control; stability; stochastic systems; Markov processes; Martingale asymptotics; Martingale limit theory; asymptotic stability analysis; ergodic theory; nontrivial stochastic adaptive control; Adaptive control; Adaptive filters; Control systems; Digital filters; Least squares approximation; Parameter estimation; Performance loss; Predictive models; Programmable control; Stochastic processes;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.45146

Filename

45146