Multi-input square iterative learning control with input rate limits and bounds

We present a simple modification of the iterative learning control algorithm of Arimoto et al. (1984) for the case where the inputs are bounded and time-rate-limited. The Jacobian error condition for monotonicity of input-error, rather than output-error, norms, is specified, the latter being insufficient to assure convergence, as proved herein. To the best of our knowledge, these facts have not been previously pointed out in the iterative learning control literature. We present a new proof that the modified controller produces monotonically decreasing input error norms, with a norm that covers the entire time interval of a learning trial.