On error convergence in adaptive iterative learning control (Q2702507)

The authors consider the linear process model NEWLINE\[NEWLINE\left\{\begin{aligned}\dot x(t)&= Ax(t) + Bu(t)\\ y(t)& = Cx(t) \end{aligned}\right.NEWLINE\]NEWLINE where \(x(t)\in\mathbb R^n\) is the state vector, with \(x(0) = x_0\), \(y(t)\in\mathbb R^m\) is the output vector, and \(u(t)\in\mathbb R^l\) is the control input vector. Stability theorems for an adaptive iterative learning control scheme are motivated and described in compact terms that relates properties of such schemes to systems structure and other important aspects of the dynamics of the process to be controlled. The use of high gain feedback in this setting is reviewed and a full proof of convergence of a universal adaptive scheme based on the use of adaptive gains in the control scheme is given. From this, it is concluded that successful iterative learning control can be achieved in the presence of substantial uncertainty in the detailed knowledge of the process parameters and order. A very important conclusion from this work is that the form and success of the controller is critically related to the process's relative degree and also its minimum-phase characteristics.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00062].