Adaptive control of a simple time-varying system

Adaptive control of a first-order randomly varying stochastic process is considered. Several authors have considered this problem recently using wither ergodic theory for Markov processes or martingale limit theorems. In both cases some initial variance calculations and bounds evaluations have to be performed in order to apply these techniques and establish the sample path results generally considered in adaptive control. The authors perform these prior calculations in the more general case where the single parameter follows a random walk and for an identification algorithm required no a priori knowledge of noise characteristics