Optimized Iterative Learning Control for Linear Discrete-Time-Invariant Systems

In this paper, an optimized first-order iterative learning control (OILC) scheme is explored for a class of linear discrete-time-invariant systems with Markov parameters available and the system relative degree being unity. For the OILC scheme, the iteration-time-variable derivative learning-gain vector is argued by sequentially minimizing the sum of the tracking error energy and the learning effort intensity amplified by an iteration-wise tuning factor. In virtue of the optimization criterion, the existence and the uniqueness of the iteration-time-variable learning-gain vector is achieved. Then, by making use of the elementary transformations which exchange the rows and columns of a matrix and by taking advantage of the positivity relationship of the eigenvalues with the matrix-weighing quadratic function, the strictly monotone convergence of the OILC scheme is derived, which conveys that the strict monotonicity is guaranteed without any requirement to the system Markov parameters and the convergence rate is adjustable by scaling the tuning factor. Furthermore, an optimized higher-order iterative learning control mechanism is developed for the system relative degree is larger than unity, for which the existence and the uniqueness of the optimized higher-order iteration-time-variable learning-gain vector are discussed and the strictly non-conditional monotone convergence is analyzed. The numerical simulations demonstrate the validity and effectiveness.