Iterative learning control for two-dimensional linear discrete systems with Fornasini-Marchesini model

Convergence Analysis of Iterative Learning Control for Two Classes of 2-D Linear Discrete Fornasini–Marchesini Model

“…e independent indexes n 1 and n 2 in practical 2-D LDFFM, i.e., chemical reactors, heater exchangers, and pipe furnaces, usually represent space locations and time instants, respectively [31]. As D � 0, 2-D LDFFM (1) has been investigated in [17,18].…”

“…(2) Compared with the adaptive ILC algorithm for 2-D LDFFM in [21,22], two ILC algorithms proposed in this paper have no restriction on the numbers of system inputs and outputs. (3) Different from the existing ILC work for 2-D LDFFM [17,18], a 3-D framework learning mechanism is presented in this paper and can reveal the dynamical behavior of the 2-D LDFFM in the horizontal dynamical direction, vertical dynamical direction, and iteration direction.…”

“…To the best of our knowledge, iterative learning control (ILC), as a data-driven and unsupervised control approach, does not require accurate knowledge of the controlled system, which makes ILC be widely prevalent in practical applications. A large number of ILC research results reported in the past few decades have fundamentally designed for one-dimensional (1-D) dynamical systems [6][7][8][9][10][11][12][13][14], only very few results involved in 2-D dynamical systems [15][16][17][18][19][20][21][22], which concentrate on mainly 2-D linear discrete first Fornasini-Marchesini model (2-D LDFFM). An optimal ILC algorithm was proposed in [16], such that the ILC tracking error converges to zero monotonically.…”

“…In [15], five ILC algorithms were proposed, the effectiveness and feasibility of which is verified through only numerical example. Afterwards, by using the column scanning approach (CSA), the iterative process of 2-D LDFFM is transformed into a iterative process of 1D systems; rigorously, theoretical proof on convergence and robustness of a two-gain ILC law is provided in [17]. Also, using the CSA as [18], to track a class of nonrepetitive reference surface described by a high-order internal model operator (HOIM), two HOIM-based ILC laws were, respectively, investigated in [23] for 2-D LDFFM by using 2-D HOIM-based linear inequality theory, but the ultimate ILC tracking error can only converge to a bounded range.…”

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

“…In practice, the random uncertainties in boundary condition and reference trajectory are inevitable due to the complicated environment. Thus, when one of the boundary conditions was set to be iteration-variant, a robust ILC law was introduced in [11]. Furthermore, when random uncertainties in boundary condition and reference trajectory were both considered, authors in [10] proposed an adaptive ILC for 2-D FMM systems.…”