Iterative Rectifying Methods for Nonrepetitive Continuous-Time Learning Control Systems

To implement iterative learning control (ILC), one of the most fundamental hypotheses is the strict repetitiveness (i.e., iteration-independence) of the controlled systems, especially of their plant models. This hypothesis, however, results in difficulties of developing theoretic analysis methods and promoting practical applications for ILC, especially in the presence of continuous-time systems, which is the motivation of the current paper to cope with robust tracking problems of continuous-time ILC systems subject to nonrepetitive (i.e., iteration-dependent) uncertainties. Based on integrating an iterative rectifying mechanism, continuous-time ILC can effectively address the ill effects of the multiple nonrepetitive uncertainties that arise from the system models, initial states, load and measurement disturbances, and desired references. Furthermore, a robust convergence analysis method is presented for continuous-time ILC by combining a contraction mapping-based method and a system equivalence transformation method. It is disclosed that regardless of continuous-time ILC systems with zero or nonzero system relative degrees, the robust tracking tasks in the presence of nonrepetitive uncertainties can be accomplished, together with the boundedness of all the system trajectories being ensured. Two examples are included to verify the validity of our robust tracking results for nonrepetitive continuous-time ILC systems.