Stability, convergence, and robustness of deterministic multivariable self-tuning control

Self-tuning control is an important approach to intelligent control system design because this kind of control system uses online parameter estimation (or learning) to derive the model of the plant, and as a result of model parameter estimation (or learning), the controller parameters can be adjusted online. However, we still lack a unified analysis tool (which is independent of specific controller design strategy and parameter estimation algorithm) that can be used by engineers to easily understand and judge the stability, convergence, and robustness of this kind of self-tuning control system. This study is focused on a unified analysis of deterministic multivariable self-tuning control systems with the help of the virtual equivalent system (VES) approach based on the transfer function concept. For different parameter estimation situations (three cases are considered, i.e., parameter estimation converges to its true value, parameter estimation converges to other values, and parameter estimation does not converge), four theorems and two corollaries on the stability, convergence, and robustness of deterministic multivariable self-tuning control systems are given with some remarks. These results are independent of specific controller design strategy and parameter estimation algorithm. From the results obtained in this study, it is concluded that the convergence of parameter estimates is unnecessary for the stability and convergence of a self-tuning control system. The feedback information of the self-tuning control system itself is sufficient to achieve the control objective, i.e., the external excitation signal is unnecessary for the deterministic multivariable self-tuning control system. Moreover, on the basis of the results of the stability, convergence, and robustness of deterministic multivariable self-tuning control systems, we have obtained a profound understanding of the self-tuning control system design method. This understanding will provide more flexibility for engineers in real applications of this kind of controller design strategy.