On the convergence of self-tuning stochastic servo algorithms based on stochastic approximation

The problem of the adaptive tracking of stochastic reference signals is considered, supposing that the process can be represented by an ARMAX model with arbitrary time delay and the reference signal by an ARMA model. Two algorithms of the stochastic approximation type, providing adaptation to both process and reference characteristics, are proposed. They differ by the incorporated a priori knowledge about the optimal regulator parameters. Global stability, asymptotic optimally, convergence of the adaptive control law in a Cesaro sense, and the strong consistency of the parameter estimates are proved. The persistence-of-excitation condition is analyzed