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Convergence rate of least-squares identification and adaptive control for stochastic systems. (English) Zbl 0604.93061
The paper considers multivariable (MIMO) ARMAX models whose parameters are estimated by the so-called extended least-squares (ELS) method (also called approximate maximum likelihood method, or pseudo-linear regression method). Under the usual positive realness condition and some other mild conditions, some results on the convergence rates for the parameter estimation error are derived. These results are subsequently used to analyse the performance of an adaptive control system with quadratic cost and ELS identifier. The rate of convergence of the cost to its minimal value is established.
Reviewer: P.Stoica

MSC:
93E12 Identification in stochastic control theory
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
93C40 Adaptive control/observation systems
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
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