Observer-based Iterative Learning Control for a Class of Time-Varying Nonlinear Systems

In this brief, we propose an observer-based iterative learning control (ILC) scheme for the tracking problem of a class of time-varying nonlinear systems. First, a state observer is derived for the system under consideration, and sufficient conditions for the boundedness and the convergence to zero of the estimation error are given. Thereafter, an iterative learning rule—based on the proposed state observer—ensuring the boundedness of the tracking error is derived. Moreover, it is shown that if the initial state variables are known, it is possible to obtain a perfect convergence to zero, over a finite tracking horizon, when the number of iterations tends to infinity. By associating a state observer with the ILC scheme it is possible to avoid the use of state and output time-derivative measurements which are generally necessary in contraction mapping based ILC design for nonlinear systems without zero relative degree.