Adaptive ILC of Tracking Nonrepetitive Trajectory for Two-dimensional Nonlinear Discrete Time-varying Fornasini-Marchesini Systems with Iteration-varying Boundary States

Robust decentralized iterative learning control for large‐scale interconnected systems described by 2‐D Fornasini–Marchesini systems with iteration‐dependent uncertainties including boundary states, disturbances, and reference trajectory

“…In particular, if these iteration‐dependent uncertainties are convergent progressively along the iteration direction, the ILC tracking error can converge to zero. The main contributions of this article are summarized as follows:Compared with all the existing ILC results on the LSIS with finite subsystems described by 1‐D dynamical systems, in this article, it is the first time to investigate ILC algorithms for the LSIS composed of finite subsystems described by 2‐D linear discrete Fornasini–Marchesini systems with iteration‐dependent uncertainties. Different from the existing adaptive ILC algorithm for 2‐D discrete Fornasini–Marchesini systems in References 17,18,21, in this article, the ILC algorithm considered has no limitations on the numbers of control inputs and system outputs. The existing ILC algorithms for 2‐D discrete systems are difficult to be applied to the LSIS composed of finite subsystems described by 2‐D linear discrete Fornasini–Marchesini systems. To this end, a modified ILC law with compensation technique is proposed in this article.…”

An Accelerated Error Convergence Design Criterion and Implementation of Lebesgue-p Norm ILC Control Topology for Linear Position Control Systems

“…In [44], to make the iterative learning control algorithm convergent in the sense of upperbounded norm measurement, the algorithm is adjustable and learning law subinterval modified accordingly. However, the algorithm structure is quite complex, and it is not easy to apply in practical nonlinear engineering systems [45].…”

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

“…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.…”

“…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. To this end, adaptive ILC approach was proposed in [21,22] to identify all unknown system parameters of 2-D LDFFM, and the ILC result of perfect tracking on iterationvarying reference surface can be obtained. Unfortunately, the gain matrix in 2-D LDFFM is required to be positive definite, such that the proposed adaptive ILC algorithm, in practical applications, is greatly restricted.…”

“…To the best of our knowledge, it is the first time to investigate ILC algorithms for 2-D LDFFM with a direct transmission from inputs to outputs and for 2-D LDFFM with input delay. (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.…”