An Upper Limit for Iterative Learning Control Initial Input Construction Using Singular Values

Selecting a proper initial input for Iterative Learning Control (ILC) algorithms has been shown to offer faster learning speed compared to the same theories if a system starts from blind. Iterative Learning Control is a control technique that uses previous successive projections to update the following execution/trial input such that a reference is followed to a high precision. In ILC, convergence of the error is generally highly dependent on the initial choice of input applied to the plant, thus a good choice of initial start would make learning faster and as a consequence the error tends to zero faster as well. Here in this paper, an upper limit to the initial choice construction for the input signal for trial 1 is set such that the system would not tend to respond aggressively due to the uncertainty that lies in high frequencies. The provided limit is found in term of singular values and simulation results obtained illustrate the theory behind.