Extremum seeking-based perfect adaptive tracking of non-PE references despite nonvanishing variance of perturbation

This paper presents a novel algorithm for adaptive stabilization of unstable discrete time systems with unknown control directions. In a departure from commonly used recursive least squares and gradient type parameter estimators, the proposed algorithm is based on extremum seeking (ES) method. The perturbation signal is a martingale difference sequence (m.d.s) with a non-decaying (bounded from below) variance. In spite of a non-vanishing perturbation, somewhat surprisingly it is shown that globally, almost surely (a.s.) the tracking error converges to zero, input and output signals are uniformly bounded, and the parameter estimates are convergent sequences.