Study on the robustness and the convergence properties of iterative learning controller

Abstract

For more robust and reliable iterative learning control systems, the following two important issues of the learning control are considered in this dissertation : the robustness issue to the initial error and the convergence issue in the sense of sup-norm. The main theme of this dissertation is how to design a iterative learning controller in order to make the learning algorithm to be more robust to the initial error and/or guarantee the exponential convergence in the sense of the sup-norm. To this end, we restrict our attention to the PD-type learning law and study its properties about the two issues. Based on the investigated properties of PD-type learning law, the design guide-line will be developed for the selection of the learning gain. First, we investigate some effects of errors in the initial conditions as a learning control algorithm is iteratively applied. In order to handle the robustness issue in more systematic way, this issue is discussed on the two cases, that is, the same initial error case and variable initial error case. In the same initial error case, it is shown that the resulting output trajectory can be exactly estimated by the design parameter of the learning law and the initial state error. For the variable initial error case, we show that the pure error term in the learning control law can be positively utilized to improve the system performance to be robust against varying initial conditions. For better performance in the face of variable initial conditions, we propose a method of `iterative learning control with multi-modal input``. In this proposed control method, an input is synthesized based on the state of initial condition. Second, we report that huge overshoot may be observed in the output trajectory error even though the applied learning algorithm is proved to be exponentially convergent with respect to the $\lambda$-norm. This is due to the discrepancies in the way of convergence in the sense of $\lambda$-norm and of sup-norm. ...