Iterative learning control is an intelligent control algorithm which imitates human learning process. Based on this concept, this paper discussed iterative learning control problem for a class parabolic linear distributed parameter systems with uncertainty coefficients. Iterative learning control algorithm with forgetting factor is proposed and the conditions for convergence of algorithm are established. Combining the matrix theory with the basic theory of distributed parameter systems gives rigorous convergence proof of the algorithm. Finally, by using the forward difference scheme of partial differential equation to solve the problems, the simulation results are presented to illustrate the feasibility of the algorithm. 1. Introduction Iterative learning control (ILC) is an intelligent control method for systems which perform tasks repetitively over a finite time interval. Since the original work by Arimoto et al. [1], in the last three decades, ILC has been constantly studied. Currently, the iterative learning control (ILC) problem for lumped parameter systems which describes ordinary differential equations has been studied continuously, and very rich theory results are obtained [2–5]. Meanwhile, owning to the ILC method is also suitable to some systems which possess model uncertainty and nonlinear characteristics, so in practice ILC has also been widely applied; for example, ILC has been applied successfully in industrial robots, intelligent transportation systems, injection process, biomedical engineering, aspects of steelmaking, and tobacco fermentation systems and has obtained great economic benefit [6–10]. The main benefit of ILC is that for the design of control law not much information about the plant is required and it may even be completely unknown, it only requires the tracking references and input/output signals. However, the algorithm is simple and effective [11–13]. Recently, iterative learning control problem of distributed parameter systems described by partial differential equations has become a hot research. In [14], the ILC method was used on temperature control of the nonisothermal turbulence chemical reactor which has a first-order hyperbolic distributed parameter systems characteristics. Qu further applied iterative learning control to a flexible system described by a class of second order hyperbolic equations at in [15]; Zhao and Rahn discussed the ILC of distributed parameter systems control problems in the material transportation system [16], and its learning control laws act to the system boundary. Based on the operator
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