Asymptotically Optimal Adaptive Control with Consistent Parameter Estimates

Abstract

For the discrete-time linear stochastic systems with unknown coefficients we give an adaptive control by which both strong consistency of the parameter estimates and asymptotic optimality for the tracking system are achieved simultaneously. This is done by disturbing the signal that is to be tracked, and the disturbance consists of a sequence of random vectors with covariance matrices tending to zero. The main result is essentially based on some criteria for consistency of parameter estimate for the system without monitoring, which are also demonstrated in the paper. The existence of adaptive control is also discussed.