Stochastic P-type/D-type iterative learning control algorithms

This paper presents stochastic algorithms that compute optimal and sub-optimal learning gains for a P-type iterative learning control algorithm (ILC) for a class of discrete-time-varying linear systems. The optimal algorithm is based on minimizing the trace of the input error covariance matrix. The state disturbance, reinitialization errors and measurement errors are considered to be zero-mean white processes. It is shown that if the product of the input-output coupling matrices C(t + 1)B(t) is full column rank, then the input error covariance matrix converges to zero in presence of uncorrelated disturbances. Another sub-optimal P-type algorithm, which does not require the knowledge of the state matrix, is also presented. It is shown that the convergence of the input error covariance matrices corresponding to the optimal and sub-optimal P-type and D-type algorithms are equivalent, and all converge to zero at a rate inversely proportional to the number of learning iterations. A transient-response performance comparison, in the domain of learning iterations, for the optimal and sub-optimal P- and D-type algorithms is investigated. A numerical example is added to illustrate the results.