Iterative Learning Control for discrete nonlinear systems with randomly iteration varying lengths

Shen, Dong; Zhang, Wei; Xu, Jian‐Xin

doi:10.1016/j.sysconle.2016.07.004

Cited by 89 publications

(84 citation statements)

References 13 publications

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“…Such mechanisms can be combined with the results given in this paper to deal with the initial resetting issue. Besides, if the initial state is not identically reset but locates in a bounded range around x d (0), then one can obtain that the tracking error converges to a small zone around zero similarly to [30].…”

Section: Problem Formulationmentioning

confidence: 98%

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Iterative Learning Control for Nonlinear Systems with Data Dropouts at Both Measurement and Actuator Sides

Jin¹,

Shen²

2017

Asian Journal of Control

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This paper discusses the iterative learning control (ILC) for nonlinear systems under a general networked control structure, in which random data dropouts occur independently at both measurement and actuator sides. Both updating algorithms are proposed for the computed input signal at the learning controller and the real input signal at the plant, respectively. The system output is strictly proved to converge to the desired reference with probability one as the iteration number goes to infinity. A numerical simulation is provided to verify the effectiveness of the proposed mechanism and algorithms.

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Section: Problem Formulationmentioning

confidence: 98%

“…This technique can be applied to deal with other similar random factors in ILC such as iteration-varying lengths [30]. Roughly speaking, this modification can effectively handle the newly introduced randomness (or asynchronization), which is generated by the random data dropouts at both measurement and actuator sides.…”

Section: Remarkmentioning

confidence: 99%

Iterative Learning Control for Nonlinear Systems with Data Dropouts at Both Measurement and Actuator Sides

Jin¹,

Shen²

2017

Asian Journal of Control

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“…In the existing papers, the absent tracking error is usually made up by appending zeros to the absent time t ∈ (T i , T] to establish a formulation of ILC algorithm. [12][13][14][15][16][17][18] Differing from these papers, the virtual tracking error of the remaining unstepped part of the iteration interval is compensated by keeping the value at time instant T i . In particular, we define the piecewise function for the kth-dimension of the virtual tracking error as…”

Section: Design Of the Controllermentioning

confidence: 99%

Adaptive learning control for general nonlinear systems with nonuniform trial lengths, initial state deviation, and unknown control direction

Liu

Shen

Wang

2019

Intl J Robust & Nonlinear

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Summary This paper studies the iteration varying trail lengths problem for high‐order continuous‐time nonlinear systems, where the initial state may deviate from the desired value and the sign of input gain is unknown. First, to deal with the general nonlinear systems, a fuzzy approximation technique is applied for each dimension of the nonlinear function and the backstepping technique is then used for controller design and performance analysis. Moreover, to deal with the randomly varying trial length problem, we introduce a novel composite energy function for the asymptotic convergence analysis. Furthermore, the initial state deviation issue is resolved by introducing an initial state learning protocol such that the initial state tracking error converges to zero asymptotically. Last but not least, the unknown control direction is regulated by applying a Nussbaum function and the analysis in the presence of nonuniform trial lengths is strictly established. Based on these treatments, we prove that the tracking error converges to zero as iteration number increases and all signals are bounded. The effectiveness of the proposed framework is verified by numerical simulations.

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“…[16][17][18][19][20][21][22][23][24][25][26][27][28] For instance, Li et al [21][22][23] introduce a newly defined stochastic variable and an iteration-average operator into ILC algorithm to deal with the randomly varying trial lengths of both discrete-time linear and continuous-time nonlinear systems, where the convergence of the tracking error is derived in the sense of mathematical expectation. Motivated by the works of Li et al, [21][22][23] Shen et al 24 extend ILC with variable pass lengths to a class of discrete-time nonlinear systems. Furthermore, Shen et al 25,26 derive the convergence of a P-type updating law with nonuniform trial lengths in the sense of almost sure and mean square.…”

Section: Introductionmentioning

confidence: 99%

Sampled‐data iterative learning control for continuous‐time nonlinear systems with iteration‐varying lengths

Wang

Shen

2018

Intl J Robust & Nonlinear

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In this work, sampled-data iterative learning control (ILC) method is extended to a class of continuous-time nonlinear systems with iteration-varying trial lengths.In order to propose a unified ILC algorithm, the tracking errors will be redefined when the trial length is shorter or longer than the desired one. Based on the modified tracking errors, 2 sampled-data ILC schemes are proposed to handle the randomly varying trial lengths. Sufficient conditions are derived rigorously to guarantee the convergence of the nonlinear system at each sampling instant.To verify the effectiveness of the proposed ILC laws, simulations for a nonlinear system are performed. The simulation results show that if the sampling period is set to be small enough, the convergence of the learning algorithms can be achieved as the iteration number increases. KEYWORDSinitial state condition, iteration learning control, iteration-varying lengths, iteratively moving average operator, relative degree, sampled-data Int J Robust Nonlinear Control. 2018;28:3073-3091.wileyonlinelibrary.com/journal/rnc

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Iterative Learning Control for discrete nonlinear systems with randomly iteration varying lengths

Cited by 89 publications

References 13 publications

Iterative Learning Control for Nonlinear Systems with Data Dropouts at Both Measurement and Actuator Sides

Iterative Learning Control for Nonlinear Systems with Data Dropouts at Both Measurement and Actuator Sides

Adaptive learning control for general nonlinear systems with nonuniform trial lengths, initial state deviation, and unknown control direction

Sampled‐data iterative learning control for continuous‐time nonlinear systems with iteration‐varying lengths

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