Design of Adaptive ILC for 2-D FMM Systems With Unknown Control Directions

Abstract

Among the existing adaptive iterative learning control (ILC) work concerning unknown control direction problem, no result is available for the two-dimensional (2-D) dynamical systems. In this paper, an adaptive ILC is developed for a class of 2-D dynamical systems described by the Fornasini-Marchesini model (FMM). Notably, the 2-D FMM system under investigation possesses not only random uncertainties in boundary condition and reference trajectory, but also unknown control direction. Even so, the constructed adaptive ILC combining with a modification mechanism can still guarantee the precise tracking of iteration-variant reference trajectory and the boundedness of all the system signals, as iteration number k tends to infinity. Theoretical analysis and simulation study are given to demonstrate the effectiveness of the developed adaptive ILC.

Keywords

• Two-dimensional (2-D) dynamical systems
• unknown control direction
• adaptive iterative learning control (ILC)
• the Fornasini-Marchesini model (FMM)