Time-Scale Transformed Iterative Learning Control for a Class of Nonlinear Systems With Uncertain Trial Duration

Iterative learning control (ILC) is a powerful tool for improving the tracking performance in systems characterized by trial-repetitive behavior, including exogenous signals such as references and disturbances, through repeated update of control signals based on previous error histories. The application of ILC algorithms to physical systems typically requires trial-to-trial invariance that is expressed as a set of assumptions on the operation of the process. Among these assumptions is that the duration of the system trajectory is trial-invariant. In some physical processes, however, the trial duration may be a function of system outputs or states that may force the trial to be either shorter or longer than expected. This results in situations in which the trial duration is unknown a priori, breaking the typical invariance assumptions, but in which updating the control input is still desired. In order to address this class of processes, the approach proposed here uses a time-scale transformation to nondimensionalize the trial duration. An ILC algorithm is then proposed on the nondimensional time scale, and it is shown that the output error converges asymptotically toward the origin. A learning operator design is proposed, which provides a direct tradeoff between convergence rate and steady-state error. Simulation results on a benchmark nonlinear system demonstrate the efficacy of the proposed approach.