Fractional order iterative learning control for fractional order system with unknown initialization

Li, Yan; Chen, YangQuan; Ahn, Hyo‐Sung

doi:10.1109/acc.2014.6859010

Cited by 12 publications

(5 citation statements)

References 31 publications

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“…Moreover, memory signifies that the non-zero history function is necessarily to be considered in fractional order system identification [33] [34]. Besides, the short memory principle can be applied to implement the initialization by using finite data.…”

Section: Fractional Order Initialized Systemmentioning

confidence: 99%

Memory identification of fractional order systems: Background and theory

Zhao

2015

The 27th Chinese Control and Decision Conference (2015 CCDC)

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This paper presents a novel work that how to determine the memory (initialization function) of fractional order systems by using the recent sampled input-output data. The background and basic theories of initialized fractional order systems are introduced. A practical algorithm is proposed to estimate the initial value of initialization function, which is adaptive to all system parameters. A P-type learning law is applied so that the initialization function can be computed accordingly. The whole process is optimized by using finite system information. The above strategy is available for both Caputo and Riemann-Liouville fractional order systems, where the initial values are applied instead of the initial conditions.

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Section: Fractional Order Initialized Systemmentioning

confidence: 99%

Memory identification of fractional order systems: Background and theory

Zhao

2015

The 27th Chinese Control and Decision Conference (2015 CCDC)

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“…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%

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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“…The possibility of application to the motion control of robot manipulators was discussed under specific conditions. Moreover, the D α -type FOILC scheme was applied to a the fractional order linear system with different historical functions under the Riemann-Liouville definition [26], and the relationship between memory and convergent performance was highlighted. Lan [27] presented a P-type ILC scheme with initial state learning for a single-inputCsingle-output fractional order nonlinear system, and the asymptotic stability of PD α -type ILC was studied by Li et al [28].…”

Section: Introductionmentioning

confidence: 99%

Iterative Learning Control for Fractional order Nonlinear System with Initial Shift

Zhou

Wang

2021

Preprint

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In this study, a closed-loop Dα -type iterative learning control(ILC) with a proportional D-type iterative learning updating law for the initial shift is applied to nonlinear conformable fractional system. First, the system with the initial shift is introduced. Then, fractional-order ILC (FOILC) frameworks that experience the initial shift problem for the path-tracking of nonlinear conformable fractional order systems are addressed. Moreover, the sufficient condition for the convergence of tracking errors is obtained in the time domain by introducing λ -norm and Hölder’s inequality. Lastly, numerical examples are provided to illustrate the effectiveness of the proposed methods.

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Fractional order iterative learning control for fractional order system with unknown initialization

Cited by 12 publications

References 31 publications

Memory identification of fractional order systems: Background and theory

Memory identification of fractional order systems: Background and theory

Convergence Analysis of Iterative Learning Control for Initialized Fractional Order Systems

Iterative Learning Control for Fractional order Nonlinear System with Initial Shift

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