On the stability and convergence of self-tuning control systems (II) - stochastic plant

This paper attempted to address the open problem - a general theory of parameter adaptive control (stochastic plant). Similar to the deterministic situation, three criteria on the stability and convergence of stochastic self-tuning control systems are presented, with which a unified analysis of stochastic self-tuning control systems is carried out. Specifically, two criteria are used to judge the stability and convergence of stochastic 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 minimum variance self-tuning control systems with arbitrary parameter estimation algorithms. We wanted to show that virtual equivalent system concept and methodology is a potential approach towards a general theory of adaptive control.