Fractional-order iterative learning control for fractional-order systems with initialization non-repeatability

Xu, Xiaofeng; Chen, Jinshui; Lu, Jiangang

doi:10.1016/j.isatra.2023.09.028

Cited by 2 publications

(3 citation statements)

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“…In addition, since ε in,k is proportional to ∥ δx k (0) ∥ ∞ and ∥ δΨ k ∥ λ , and ultimately determined by δϕ k according to (40), the tracking performance can be improved by reducing the initialization shift. In this regard, the preconditioning based initialization strategy [28] is noteworthy, as it can eliminate initial shift and reduce ∥ δΨ k ∥ λ .…”

Section: Remarkmentioning

confidence: 99%

“…From Figure 2a,c, it can be observed that the tracking error of u and i remain bounded, and the convergence process are presented in Figure 2b,d. It should be noted that i k fluctuates significantly near t = 0 due to the iteration-varying ϕ k and u k (0) [28]. Thus, the root-mean-square (RMS) value of δi k (t) is adopted to measure the input performance on the entire [0, 1], and the maximum absolute value of δu k (t) is applied to evaluate the output performance.…”

Section: Examplementioning

confidence: 99%

“…In this regard, refs. [27,28] proposed a system preconditioning strategy based on the short memory principle to improve the system performance and then derived the ILC convergence condition. However, this ILC scheme cannot achieve perfect tracking performance, and the preconditioning operation requires additional time cost.…”

Section: Introductionmentioning

confidence: 99%

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Convergence Analysis of Iterative Learning Control for Initialized Fractional Order Systems

Xu,

Lu,

Chen

2024

Fractal Fract

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Iterative learning control is widely applied to address the tracking problem of dynamic systems. Although this strategy can be applied to fractional order systems, most existing studies neglected the impact of the system initialization on operation repeatability, which is a critical issue since memory effect is inherent for fractional operators. In response to the above deficiencies, this paper derives robust convergence conditions for iterative learning control under non-repetitive initialization functions, where the bound of the final tracking error depends on the shift degree of the initialization function. Model nonlinearity, initial error, and channel noises are also discussed in the derivation. On this basis, a novel initialization learning strategy is proposed to obtain perfect tracking performance and desired initialization trajectory simultaneously, providing a new approach for fractional order system design. Finally, two numerical examples are presented to illustrate the theoretical results and their potential applications.

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Section: Remarkmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%