Iterative learning control of complex Ginzburg–Landau system

Abstract

Different from the existing research on iterative learning control (ILC) real-valued systems, complex-valued partial differential system is studied in this paper. All variables and parameters of the system are complex, and distributed control is imposed on the system. First, the original complex system is transformed into two coupled real systems, which represent the real and imaginary parts of the original complex system, respectively. Second, a complex [Formula: see text]-type ILC algorithm is designed that the real and imaginary parts of the learning law are coupled to each other. Then, the contraction mapping principle and analytical techniques are used to ensure that the tracking error converges to zero in the sense of [Formula: see text]-norm. Finally, a numerical simulation is presented to show the effectiveness of the proposed algorithm.