Martingale hyperconvergence theorem and convergence of robust output tracking for time-varying systems

Stability of adaptive control for time-varying systems (TVS) is surveyed and then a powerful mathematical tool-martingale hyperconvergence theorem-is presented which can be successfully applied to analyze the convergence of various identification algorithms and adaptive control algorithms for TVS. It makes an important advance in the study of the convergence and stability problems of TVS. The analysis indicates that the output tracking error given by adaptive control based on the projection algorithm is consistently bounded. The authors state that this is the best convergence result in the area of adaptive control for time-varying systems up to now