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Stochastic adaptive prediction and model reference control. (English) Zbl 0827.93071

The authors propose a comprehensive theory of stochastic adaptive filtering, control and identification. They analyze two identification algorithms each for two possible parametrizations of the system and indirect and direct adaptive predictors each based on either a least- square or a gradient algorithm. In addition to analyzing similar direct adaptive control algorithms, the authors propose a new and general method for deducing adaptive controller parameter convergence. They show that the parameter estimates converge to the null space of a certain covariance matrix. From this one may deduce the convergence of several particular adaptive controllers.

MSC:

93E35 Stochastic learning and adaptive control
93C40 Adaptive control/observation systems
93E12 Identification in stochastic control theory
93C55 Discrete-time control/observation systems
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