Iterative learning control for non-linear systems with deadzone input and time delay in presence of measurement noise

The main purpose of this study is to propose an iterative learning control (ILC) algorithm for non-linear systems with dead-zone input and time delay in presence of measurement noise. The dead-zone non-linearity is described by a general model and all parameters of the dead-zone are unknown. The state function is allowed to grow as fast as any polynomial with arbitrary order, and thus does not satisfy the global Lipschitz condition. The time delay may be time varying, and multiple time delays are also considered. It is proved that the ILC algorithm given in the study converges to the optimal one minimising the tracking error in presence of measurement noise almost surely. An illustrative numerical example is presented to show the effectiveness.