Adaptive control of a simple time-varying system

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