On a discrete-time stochastic learning control algorithm

In an earlier paper by the author (2001), the learning gain for a D-type learning algorithm, is derived based on minimizing the trace of the input error covariance matrix for linear time-varying systems. It is shown that, if the product of the input/output coupling matrices is full-column rank, then the input error covariance matrix converges uniformly to zero in the presence of uncorrelated random disturbances, whereas, the state error covariance matrix converges uniformly to zero in the presence of measurement noise. However, in general, the proposed algorithm requires knowledge of the state matrix. In this note, it is shown that equivalent results can be achieved without the knowledge of the state matrix. Furthermore, the convergence rate of the input error covariance matrix is shown to be inversely proportional to the number of learning iterations