Abstract
This paper is concerned with the minimum variance control of single-input single-output discrete-time linear stochastic systems with unknown constant parameters. A method is presented to stabilize the Self-Tuning Regulator (STR) given by Åström and Wittenmark, because the STR often causes the divergence or large peak value of the system output when the ratio of leading coefficient and its a priori estimate is not close to one.
Firstly, an admissible interval of the ratio for which the STR is stabilized is specified. Secondly, an identification algorithm of least squares type with two adjustable parameters (a. p.) is introduced, and the allowable region of the a. p. values is determined in order to ensure the global convergence of the corresponding adaptive control systems on the specified admissible interval. Lastly, a suboptimal a. p. value to suppress the output peak value is determined by maximizing a coefficient appearing in the equation used for convergence analysis. The effectiveness of the proposed method is discussed by the numerical examples in the fourth-order system.
