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Extended least squares and their applications to adaptive control and prediction in linear systems. (English) Zbl 0603.93060

Herein strong consistency of recursive extended least squares is established under considerably weaker assumptions than previously assumed in the literature. The argument used to establish consistency also leads to certain basic properties of adaptive predictors based on these recursive estimators. Making use of these properties of the adaptive predictors, simple modifications of the Åström-Wittenmark self- tuning regulator are proposed and shown to be asymptotically optimal.

MSC:

93E10 Estimation and detection in stochastic control theory
93C40 Adaptive control/observation systems
93C05 Linear systems in control theory
65C99 Probabilistic methods, stochastic differential equations
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction
93E12 Identification in stochastic control theory
93E25 Computational methods in stochastic control (MSC2010)
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