Monotone convergence rate of norm-optimal-gain-arguable iterative learning control for LDTI systems

For a class of repetitive linear discrete-time-invariant (LDTI) systems, this paper exploits a norm-optimal-gain-arguable iterative learning control (NOGAILC) scheme. For the scheme, the sequential performance index is additive quadratic norms of the tracking error vector and the incremental input vector, while the argument is the iteration-time-variable learning-gain vector. To balance the importance of the incremental input vector and the tracking error vector, the sequential tuning factors are concerned. By means of matrix theory, the learning-gain vector and the convergence rate are explicated that indicate that both the tracking error and the optimal performance index are linearly monotonically convergent and the NOGAILC with a smaller tuning factor delivers a faster convergence. Further, for the system parameters existing uncertainties, a quasi-NOGAILC profile is established and the time-domain rigorous derivation conveys that the quasi-scheme is linearly monotonically convergent for the parameters uncertainties within a wider range. Numerical simulations testify the validity and the effectiveness.