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Self-tuning controls of linear stochastic systems in presence of drift. (English) Zbl 0654.93040
Summary: This paper deals with self-tuning controls constructed by inserting the estimates for the unknown parameters. The model of a linear control system containing a constant drift is considered. The unknown parameters are estimated by the least squares method. A recursive formula for the estimates is introduced and a sufficient condition for its consistency is presented. Assuming consistency, the asymptotic distributions of the estimates and of the quadratic functionals are investigated. From the asymptotic distributions the quality of the self-tuning can be assessed. At the end two examples are included for illustration.

MSC:
93C40 Adaptive control/observation systems
93C05 Linear systems in control theory
60J60 Diffusion processes
93E10 Estimation and detection in stochastic control theory
62E20 Asymptotic distribution theory in statistics
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