Finite-Iteration Learning Control for Nonlinear Systems with Parameter Uncertainties

For most of the existing iterative learning control (ILC) results, the tracking of the target trajectory is achieved asymptotically as the iteration number tends to infinity. In this study, a finite-iteration learning control (FILC) strategy is proposed to achieve the accurate tracking of trajectory in a finite iteration number. As the first study of FILC, a linear parameterized system with parameter uncertainties is considered in this article. To eliminate the influence of unknown parameters, we first design a parameter update law. The true value of the unknown parameter is estimated in a finite iteration number by using the proposed parameter update law. Then, with the help of the true value of unknown parameter, a novel fractional-power structure control law with a iteration-varying control gain is designed. Under the proposed FILC scheme, the tracking of target trajectory is achieved in a finite-iteration number. The computation method of the iteration number is given. Illustrative examples are provided to verify the theoretical results.