Linearly monotonic convergence of nonlinear parameter‐optimal iterative learning control to linear discrete‐time‐invariant systems

Abstract

AbstractIn this paper, a parameter‐optimal iterative learning control (POILC) scheme is developed for linear discrete‐time‐invariant systems with Markov parameters available. For the scheme the iteration‐time‐variable learning‐gain vector is assigned as the argument while the sequential performance index is consisting of the quadratic tracking error energy plus quadratic learning effort intensity weighed by the iteration‐varying tuning factor. By making use of matrix theory, the learning‐gain vector and the convergence rate are explicated which conveys that the POILC is a nonlinear scheme and is linearly monotonously convergent with the smaller tuning factors delivering the faster convergence. In particular, the linearly monotone convergences are respectively exploited for the extreme case when the tuning‐factor sequence is identically nullity and for the optimal performance index. Further, a quasi POILC is established which considers additive systematic parameters uncertainties in composing of the learning‐gain vector. Rigorous analysis indicates that the quasi POILC is linearly monotonically convergent within a wider uncertainty range which conveys that the POILC is robust to the system parameters uncertainties. Numerical simulations testify the validity and the effectiveness.