ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

Abstract

This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…Many scholars have studied the initial state of iterative learning [24,25,[27][28][29]. In [24], for a class of nonlinear systems running repeatedly in the study of the convergence of iterative learning control, a PID fuzzy iterative learning control algorithm has been proposed in the arbitrary initial state.…”

“…[27] presents a P-type ILC scheme with initial state learning for a class of α fractional-order nonlinear system. In [28], the paper presents a second order P-type ILC scheme with initial state learning for a class of fractional order linear distributed parameter systems. In [29], the study addresses a robust ILC scheme for non-linear discrete-time systems in which both the trail lengths and the initial state shifts could be randomly variant in iteration domain.…”