On the self-tuning regulator and a priori ELS convergence

It is only now, after one decade of adaptive control theory development following on from the self-tuning-regulator (STR) algorithms of Astrom and Wittenmark, that the original insights imbedded in its design are justified by a rigorous global convergence theory, as outlined in the paper. The original STR is of current interest from a theoretical point of view because it is the first example of a direct adaptive stochastic control scheme for which the plant noise, when present, is sufficient to achieve the persistence of excitation required for asymptotic optimality. This aspect is featured in the theory of the paper. The theory of the paper also generalizes open-loop extended least squares (recursive maximum likelihood) global convergence theory to the case where state estimates involving a priori noise estimates are employed rather than a posteriori ones as in existing theories.