A survey of some results in stochastic adaptive control.

*(English)*Zbl 0571.93038Some 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.

##### MSC:

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 |