Convergence rate for RLS-based direct self-tuning minimum-variance regulation of ARMAX minimum phase plants

An upper bound for the error convergence rate of recursive least squares (RLS)-based direct self-tuning minimum-variance (DSTMV) regulation of minimum phase multiple time-delay autoregressive moving average with exogenous input (ARMAX) plant is derived. The RLS algorithm used is k-interlaced, with k being the plant time-delay. The bound is derived for known fixed b/sub 0/ by extending a previously proposed methodology. The bound provides a joint explanation of DSTMV regulation stability and parameter estimate convergence. The paper demonstrates that self-tuning is based on convergence properties of RLS as well as on the excitation quality of plant white noise, which generates (via controller feedback) the plant input.