Iterative Learning Control for MIMO Singular Distributed Parameter Systems

Abstract

This paper deals with the iterative learning control issue for multi-input multi-output singular distributed parameter systems (SDPSs) with parabolic and hyperbolic type, which described by coupled partial differential equations with singular matrix coefficients. Initially, applying the singular value decomposition theory to SDPSs, an equivalent dynamic decomposition form is derived. Then, the estimation of the relationship between the learning system substates and output tracking error are constructed in the light of P-type update learning scheme under some assumptions. Moreover, two sufficient conditions are presented to ensure that the tracking error is convergent in the sense of L2 norm by employing the contracting mapping principle as well as some basic differential inequalities. Finally, two numerical examples are shown to demonstrate the validity of the developed theoretical results.

Keywords

• Distributed parameter systems
• learning systems
• intelligent control
• singular value decomposition
• convergence