Abstract
A method to design the self-tuning regulator is presented for single-input single-output linear discrete-time systems described by LS model with unknown constant parameters. The control input of the regulator is divided into the CE control input and the correction control input, and the latter is assumed to be a zero-mean white noise independent of the former. Firstly, the least squares identifier of the parameter is analyzed, and it is shown under some regularity conditions that the upper bound of the parameter estimation error is inversely proportional to the minimum eigenvalue of a matrix used in the identifier. Secondly, the relation between the eigenvalue and the variance of the correction control input is derived. Lastly, the suboptimal variance that maximize the convergence rate of the difference between the control cost predicted at each time step and its minimum value is determined as a function of the above eigenvalue. A numerical example is presented to illustrate the effectiveness of the proposed method.
