Adaptive Regulator for Hammerstein and Wiener Systems With Noisy Observations

For Hammerstein and Wiener systems observed with additive noises the adaptive regulation control is produced by a truncated stochastic approximation (SA) algorithm with truncation regions expanding with a prescribed rate. It is proved that the stochastic adaptive control given in this note is optimal in the sense that it minimizes the long run average of regulation errors a.s