Verification of the Self-Stabilization Mechanism in Robust Stochastic Adaptive Control using Lyapunov Function Arguments

The objective of this paper is to propose a new algorithm for self-tuning control in the presence of unmodeled dynamics. It is shown (with probability one) that the resulting closed-loop system is globally stable and the mean-square tracking error is proportional to the size of unmodeled dynamics. In the absence of unmodeled dynamics, the algorithm produces the minimum-variance self-timing control. It is analytically verified that the proposed algorithm has self-stabilization property, i.e., possible occurance of instability results in mean-square bounded signals.