On the stability and convergence of self-tuning control systems (I) - Deterministic plant

This paper attempted to address the open problem - a general theory of parameter adaptive control (deterministic plant). By delivering three criteria on the stability and convergence of deterministic self-tuning control systems, we show that virtual equivalent system concept and methodology might lead to a general theory for adaptive control system. Actually with the presented criteria, a unified analysis of deterministic self-tuning control systems is carried out. Specifically, two criteria are used to judge the stability and convergence of deterministic self-tuning control systems, which are independent of specific controller design strategy and specific parameter estimation algorithm. And the third criterion is used to judge the stability and convergence of one-step ahead self-tuning control with arbitrary parameter estimation algorithms.