Some aspects of the adaptive control of stochastic evolution systems

An adaptive control problem for some linear stochastic evolution systems is formulated and solved. The adaptive control problem is dichotomized into an identification problem and a control problem. For the identification of the unknown parameters, a family of least-squares estimates is shown to be strongly consistent. For the control problem the family of average costs for the optimal stationary controls based on the estimates of the unknown parameters is shown to converge to the optimal average cost. To verify this optimality, it is shown that the solution of the Riccati equation is a continuous function of the unknown parameters in the uniform operator topology