Learning-Gain-Adaptive Iterative Learning Control to Linear Discrete-Time-Invariant Systems

For a class of repetitive linear discrete-time-invariant systems with the unit relative degree, a learning-gain-adaptive iterative learning control (LGAILC) mechanism is exploited, for which the iteration-wise performance index is to maximize the declining quantity of tracking-error energies at two adjacent operations without considering control input and any parameters, and the argument is the iteration-time-variable learning-gain vector. By taking advantage of rows/columns exchanging transformations and matrix theory, an explicit learning-gain vector is solved, which exhibits that the learning-gain vector is not only dependent upon the system Markov parameters but also relevant to the iteration-time-wise tracking errors. Benefited from the orthogonality of the rows/columns exchanging transformation, it is derived that the LGAILC scheme is non-conditionally strictly monotonically convergent. For the sake of ensuring the LGAILC to be robust to the system parameters' uncertainties, a pseudo-LGAILC strategy is developed whose system Markov parameter-based learning-gain vector involves the system parameters' uncertainties. Rigorous induction delivers that the pseudo strategy is strictly monotonically convergent with a wider uncertainty degree, which implies that the pseudo strategy is robust to the system parameters' uncertainties in a wider range. The numerical simulations demonstrate the validity and effectiveness.