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.

In this paper, the iterative learning control (ILC) problem is investigated for a class of time-invariant parabolic singular distributed parameter systems. Initially, the singular distributed parameter systems is decomposed into infinite number of singular systems based on the separation principle. Meanwhile, the slow-fast subsystems are introduced via singular value decomposition method. Then, a novel mixed PD-type ILC algorithm with finite dimension is designed for the low dimensional slow part and the corresponding convergence conditions are manifested. With the proposed controller, the output error of high dimensional fast complement can satisfy the given value instead of neglecting the effect of high dimensional modes. Furthermore, under the aforesaid ILC law and the appropriate number of the low dimensional slow part, the resulting tracking error of parabolic singular distributed parameter systems can converge to any small tracking accuracy. Finally, simulation results on the distributed building automatic temperature system verify the convergence and effectiveness of the mixed PD-type ILC algorithm.

This paper presents an iterative learning identification scheme for a class of parabolic distributed parameter systems with unknown curved surfaces. The identification design method is proposed on the basis of the iterative learning concept. Initially, a new nonlinear learning identification law based on vector-plot analysis is developed to estimate the curved surface with spatial-temporal varying iteratively. Subsequently, through theoretical analysis, the sufficient convergence conditions for identification error in the sense of ${\mathbf{L}}_2$ norm is manifested. Furthermore, a high-order P-type learning law is applied to identifying the curved surface in order to compare the convergent rate with the aforesaid identification law. Finally, simulation results on a specific numerical example and the temperature profile of a catalytic rod confirm that the proposed learning identification laws is effective.