A Survey of Some Results in Stochastic Adaptive Control

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.