On almost sure and mean square convergence of P-type ILC under randomly varying iteration lengths

Shen, Dong; Zhang, Wei; Wang, Youqing; Chien, Chiang‐Ju

doi:10.1016/j.automatica.2015.10.050

Cited by 124 publications

(68 citation statements)

References 11 publications

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“…Under the proposed scheme, uniform convergence of the full state tracking errors can be guaranteed over the iteration domain, and the constraint requirement on the system output will not be violated at all time during operation. Further research in this direction can include a possible extension to MIMO nonlinear systems and stochastic systems …”

Section: Resultsmentioning

confidence: 99%

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Iterative learning control for output‐constrained nonlinear systems with input quantization and actuator faults

Jin

2017

Intl J Robust & Nonlinear

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Summary In this work, we propose a novel iterative learning control algorithm to deal with a class of nonlinear systems with system output constraint requirements and quantization effects on the system control input. Actuator faults have also been considered, which include multiplicative, additive, and stuck actuator faults. To the best of our knowledge, this is the first reported work in the iterative learning control literature to deal with quantization effects for the control input of nonlinear systems under the effects of actuator faults and system output constraints. Under the proposed scheme, using backstepping design and composite energy function approaches in the analysis, we show that uniform convergence of the state tracking errors can be guaranteed over the iteration domain, and the constraint requirement on the system output will not be violated at all time. In the end, a simulation study on a single‐link robot model is presented to demonstrate the effectiveness of the proposed scheme.

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Section: Resultsmentioning

confidence: 99%

“…Further research in this direction can include a possible extension to MIMO nonlinear systems and stochastic systems. 42,43…”

Section: Resultsmentioning

confidence: 99%

Iterative learning control for output‐constrained nonlinear systems with input quantization and actuator faults

Jin

2017

Intl J Robust & Nonlinear

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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%

“…Because the initial states are vital to ensure the repetitiveness of the system dynamics for all iterations, other works 13,14,17,[19][20][21] required that the initial states must satisfy the identical initial condition (i.i.c.). Indeed, in the ILC filed, i.i.c.…”

Section: Introductionmentioning

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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“…ILC is a kind of optimization strategy that improves the tracking performance of a system which repeatedly completes some task over a fixed time interval. Many extensive studies have covered a large range of ILC topics, including the design of update laws, identical initialization conditions, robustness, optimization, transient behavior, and the combination of ILC with other control methods [1][2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Point‐to‐Point Iterative Learning Control Based on Stochastic Approximation

Shen

Zhang³

2017

Asian Journal of Control

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An iterative learning control algorithm with iteration decreasing gain is proposed for stochastic point‐to‐point tracking systems. The almost sure convergence and asymptotic properties of the proposed recursive algorithm are strictly proved. The selection of learning gain matrix is given. An illustrative example shows the effectiveness and asymptotic trajectory properties of the proposed approach.

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On almost sure and mean square convergence of P-type ILC under randomly varying iteration lengths

Cited by 124 publications

References 11 publications

Iterative learning control for output‐constrained nonlinear systems with input quantization and actuator faults

Iterative learning control for output‐constrained nonlinear systems with input quantization and actuator faults

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

Stochastic Point‐to‐Point Iterative Learning Control Based on Stochastic Approximation

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