Adaptive control of linear delay time systems *

An adaptive control problem for linear, continuous time, discrete delay stochastic systems is described and solved in this paper. A solution of the adaptive control problem means that the family of maximum likelihood estimators are shown to be strongly consistent and te average costs are shown to converge to the optimal average cost. The unknown parameters in the model appear affinely in the drift term of the stochastic differential equation. The assumptions that are made for the solution are natural and verifiable