IEEE Transactions on Automatic Control, Vol.42, No.7, 1023-1028, 1997
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(0) by extending a recently 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.