Iterative Learning Control for MIMO Singular Distributed Parameter Systems with Parabolic Type

This paper addresses the problem of iterative learning control design for multi-input multi-output (MIMO) singular parameter distributed systems (SDPSs), which described by coupled parabolic partial differential equations with singular matrix coefficients. Initially, applying the singular value decomposition approach to SDPSs, an equivalent dynamic decomposition form is derived. Then, the estimation of the relationship between the systems state variables and output error is constructed on the basis of P-type learning law. Moreover, by employing the contracting mapping principle as well as some basic differential inequalities, a sufficient condition is presented to ensure that the L-2 norm of tracking error is convergent. Finally, a numerical simulation is shown to verify the validity of the P-type ILC algorithm.