Self-tuning control of diffusions without the identifiability condition
The self-tuning method of adaptive control for diffusions consists of estimating the unknown parameter on line and using its current estimate as the true parameter for selection of the control at each time. The a.s. optimality of this scheme for the ergodic or long-run average criterion can be established under an identifiability condition on the system, but may fail otherwise. We present a modified self-tuning scheme along the lines of the Kumar- Becker-Lin scheme for Markov chains [see \textit{P. R. Kumar} and \textit{A. Becker}, IEEE Trans. Autom. Control AC-27, 137-146 (1982; Zbl 0471.93069); \textit{P. R. Kumar} and \textit{W. Lin}, ibid., 765-774 (1982; Zbl 0488.93036)] and prove its a.s. optimality. Several heuristic issues related to this scheme are also discussed.
scientific article; zbMATH DE number 4143873
scientific article