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A survey of some results in stochastic adaptive control. (English) Zbl 0571.93038
Some results in discrete-time stochastic adaptive control are surveyed. The survey divides itself into two parts - Bayesian and non-Bayesian adaptive control. In the former area, the problems of converting an incompletely observed system into a completely observed one, multi-armed bandit processes, Bayesian adaptive control of Markov chains and Bayesian adaptive control of linear systems are exposed and surveyed. In the latter area, non-Bayesian adaptive control of Markov chains and the self- tuning regulator are dealt with. Proofs are given, where appropriate, to illustrate the methods involved.

93C40 Adaptive control/observation systems
93C55 Discrete-time control/observation systems
93E20 Optimal stochastic control
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
62A01 Foundations and philosophical topics in statistics
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