Finite difference based iterative learning control with initial state learning for a class of fractional order two‐dimensional continuous‐discrete linear systems

Abstract

This article presents a PI-type iterative learning control (ILC) law with initial state learning for a class of 𝛼 (0 < 𝛼 ≤ 1) fractional order two-dimensional (2D) linear systems. First, by using backward difference method, the finite difference approximation of the fractional order derivative is obtained, which leads to globally 2 − 𝛼 order accuracy. Then, a PI-ILC law is constructed at the nodes and the convergence analysis of the iterative scheme is proved. A linear matrix inequality-based sufficient condition is derived to guarantee that the tracking error is asymptotically convergent. The obtained convergence condition is fractional order dependent. Most of the classical ILC conditions for fractional order one-dimensional linear systems fall into the special cases of this article. Finally, the simulation results show the effectiveness of the proposed control method.

Convergence properties concerning Lebesgue‐p norm of iterative learning control for a class of fractional differential systems

“…In this work, Li et al [21] pointed out that, for an αthÀ order linear system, the order of FOILC should also be α. Based on this viewpoint, many FOILCs have been proposed to improve the control performance of various fractional-order systems in the time domain [22][23][24][25][26][27][28][29][30][31][32][33][34].…”

H∞ filtering for continuous fractional‐order 2D Roesser model: The 0<α≤1 case

“…This manuscript focuses on the $$$ {H}_{\infty } $$$ filtering problem for the continuous FO 2D Roesser model with the fractional‐order (FO) $$$ 0&lt;\alpha \le 1 $$$. The FO 2D Fornasini–Marchesini models and Roesser models have become a research hotspot recently [23–25]. Fractional calculus is the extension of integer calculus, which is one of the most powerful mathematical tools around the world [26–30].…”

Robust ∞ model reduction for the continuous fractional‐order two‐dimensional Roesser system: The 0 < ε ≤ 1 case

“…On broad time and frequency scales, fractional models that are concise and calculable can be used to analyze the FO system [31,32]. Recently, the FO 2D Fornasini-Marchesini, as well as Roesser systems, have become a focal research topic [33][34][35]. The sufficient conditions for the stability of continuous FO 2D systems Fornasini-Marchesini first model are provided in [36].…”