Fractional order nonlinear systems with delay in iterative learning control

Li, Yan; Wei, Jiang

doi:10.1016/j.amc.2015.01.014

Cited by 50 publications

(27 citation statements)

References 13 publications

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“…The analysis shows that the convergence condition is identical with the integer-order D-type ILC case when the fractional-order system and learning algorithm have the same fractional order. Further FOILCs in the time domain have been raised and convergence issues have been addressed [17][18][19][20][21][22]. In these existing FOILC investigations, the tracking errors are measured in the form of the lambda-norm, and based on the Bellman-Gronwall lemma, the convergence conditions are achieved under the premise that the parameter lambda is sufficiently larger.…”

Section: Introductionmentioning

confidence: 99%

Lebesgue‐p NORM Convergence OF Fractional‐Order PID‐Type Iterative Learning Control for Linear Systems

2017

Asian Journal of Control

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This paper discusses first-and second-order fractional-order PID-type iterative learning control strategies for a class of Caputo-type fractional-order linear time-invariant system. First, the additivity of the fractional-order derivative operators is exploited by the property of Laplace transform of the convolution integral, whilst the absolute convergence of the Mittag-Leffler function on the infinite time interval is induced and some properties of the state transmit function of the fractional-order system are achieved via the Gamma and Bata function characteristics. Second, by using the above properties and the generalized Young inequality of the convolution integral, the monotone convergence of the developed first-order learning strategy is analyzed and the monotone convergence of the second-order learning scheme is derived after finite iterations, when the tracking errors are assessed in the form of the Lebesgue-p norm. The resultant convergences exhibit that not only the fractional-order system input and output matrices and the fractional-order derivative learning gain, but also the system state matrix and the proportional learning gain, and fractional-order integral learning gain dominate the convergence. Numerical simulations illustrate the validity and the effectiveness of the results.

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Section: Introductionmentioning

confidence: 99%

Lebesgue‐p NORM Convergence OF Fractional‐Order PID‐Type Iterative Learning Control for Linear Systems

2017

Asian Journal of Control

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“…Iterative learning control methodology, which is proposed by Arimoto et al in 1984 (See [1]), is to utilize the previous control information of the studied systems. The repetitive behavior has been a major research area and a hot issue in recent years (See [2][3][4][5][6][7][8][9][10][11][12][13][14][15]).…”

Section: Introductionmentioning

confidence: 99%

“…Stabilization problem of control systems has received some research results and have been reported in the literature [3,11,13,15,[21][22][23][24][25][26][27][28][29]. However, only a few results combining with the iterative learning control items and Zhang-gradient method are available for nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

The Application of Zhang-Gradient Method for Iterative Learning Control

Zhang¹

2020

JAAM

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“…7 After developments of over 3 decades, it had been wildly used to deal with process control of artificial intelligence systems. 8,9 However, most existing literature concentrates on ordinary system, while only very a few papers [10][11][12][13][14] consider ILC for fractional-order systems, showing that much blank exists for further attention.…”

Section: Introductionmentioning

confidence: 99%

Learning formation control for fractional‐order multiagent systems

Luo

Wang

Shen

2018

Math Methods in App Sciences

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In this paper, we use 2 iterative learning control schemes (P‐type and PI‐type) with an initial learning rule to achieve the formation control of linear fractional‐order multiagent systems. To realize the finite‐time consensus, we assume repeatable operation environments as well as a fixed but directed communication topology for the fractional‐order multiagent systems. Both P‐type and PI‐type update laws are applied to generate the control commands for each agent. It is strictly proved that all agents are driven to achieve an asymptotical consensus as the iteration number increases. Two examples are simulated to verify the effectiveness of the proposed algorithms.

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Fractional order nonlinear systems with delay in iterative learning control

Cited by 50 publications

References 13 publications

Lebesgue‐p NORM Convergence OF Fractional‐Order PID‐Type Iterative Learning Control for Linear Systems

Lebesgue‐p NORM Convergence OF Fractional‐Order PID‐Type Iterative Learning Control for Linear Systems

The Application of Zhang-Gradient Method for Iterative Learning Control

Learning formation control for fractional‐order multiagent systems

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