Decentralized iterative learning control for large-scale linear discrete-time systems with fixed initial state errors

Abstract

AbstractThis article addresses the problem of iterative learning control for large-scale linear discrete-time systems with fixed initial state errors. And two kinds of the system structures are considered in this article, one of them is the system whose input signal's dimension is less than or equal to the output dimension and the other one is the system whose output signal's dimension is less than or equal to the input dimension. According to the characteristics of the systems, decentralized learning schemes are proposed for such large-scale linear discrete-time systems, and the corresponding discrete-time output limiting trajectories under the action of the decentralized learning schemes are presented. The proposed controller of each subsystem only relies on local output variables without any information exchanging with other subsystems. Using the contraction mapping method, we show that the schemes can guarantee the output of each subsystem to converge uniformly to the corresponding discrete-time output limiting trajectory over all the given discrete-time points within a finite time interval. Furthermore, the decentralized initial rectifying strategies are applied to the large-scale linear discrete-time systems for eliminating the effect of the fixed initial state errors, and the corresponding decentralized learning schemes are established. When the learning schemes are applied to the large-scale linear discrete-time systems, the output of each subsystem can converge to the desired reference trajectory of each subsystem over all the given discrete-time points within a pre-specified interval no matter what value the fixed state error takes. Simulation examples illustrate the effectiveness of the proposed method.