An iterative learning control algorithm for systems with measurement noise

We present a convergent iterative learning control (ILC) algorithm that can be used when the plant to be controlled is subject to measurement noise. The algorithm is based on previous work that exploited a multi-loop control interpretation of the signal flow in ILC to derive a necessary and sufficient condition for convergence of discrete-time, linear, time-invariant systems. The previous multi-loop approach resulted in an ILC algorithm that can converge in as few as four trials. The scheme used a deterministic adaptive gain adjustment technique (adaptive in trial number) that does not have to be “tuned”. The basis of the algorithm was online determination of the Markov parameters of the system. In the present work we extend the previous result to the case where the output measurements are corrupted by noise. In this case it is necessary to compute estimates of the (most significant) Markov parameters using parameter estimation. This parameter estimation is done in both trial number and in time, exploiting the diagonal structure of the matrix of Markov parameters. New estimates of each parameter are obtained after each trial. These estimates are then used in the derivation of the new input for the next trial, using a standard iterative learning control update algorithm. Simulations demonstrate the effectiveness of the approach