Although considerable progress has been made in stochastic adaptive control, the problem concerning the convergence of the original self-tuning regulator proposed by K.J. AAstrom and B. Wittenmark (1973) is still open. Since it is attractive in theory and important in applications, this problem is examined and a rigorous proof of its stability and optimality is given. Related problems such as convergence of the extended-least-squares (ELS)-based adaptive tracker are also considered.
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