Iterative learning control approach for linear discrete time-varying systems with different initial time points

Different from the existing iterative learning control (ILC) works for dynamical systems with iteration -varying trial lengths, in which the terminal time points are not identical, this paper presents an ILC approach for linear discrete time -varying (LDTV) systems with different initial time points. A piecewise ILC law is designed by using the segment compensation techniques in time axis. Through a rigorous mathematical analysis, it is theoretically proved that as the mathematical expectation of the iterative initial state equals to the desired initial state, the ILC tracking error at the maximum universal time interval can be driven into a bounded region in mathematical expectation sense. Particularly, the mathematical expectation of the ILC tracking error at the maximum universal time interval can even be driven to zero under a certain initial state condition. Numerical simulations are provided to verify the effectiveness of the proposed ILC scheme.