Iterative learning control using adjoint systems for nonlinear non-minimum phase systems

Most iterative learning control (PLC) using a causal updating law obtains the input given by Silverman´s (1969) or Hirshorn´s (1979) causal inversion. When the objective system is that of a non-minimum phase, we cannot use those methods because the input is exponentially increasing. To overcome this difficulty, an approach called stable inversion was proposed to give a non-causal but bounded input instead. However, no simple iterative method to obtain this non-causal input was proposed. In this paper, from a viewpoint of minimization, we develop a simple iterative method for stable inversion toward ILC for non-minimum phase systems