Adaptive ILC for tracking non-repetitive reference trajectory of 2-D FMM under random boundary condition

Xu, Qing‐Yuan; Li, Xiaodong; Lv, Mang-Mang

doi:10.1007/s12555-015-0005-3

Cited by 26 publications

(29 citation statements)

References 22 publications

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“…The learning control law of the 2D‐AILC for MIMO systems is presented as

{boldu}_{k} false(i, j false) = {\overset{Φ}{true}}_{k} false(i, j false) {boldΨ}_{k} false(i, j false), false(i, j false) \in {boldℤ}_{T_{1 normalk}} \times {boldℤ}_{T_{2 k}}

and the parameter updating law for

{\overset{Φ}{true}}_{k} false(i, j false)

is given as

{\overset{Φ}{true}}_{k} false(i, j false) = {\overset{Φ}{true}}_{k - 1} false(i, j false) + \frac{η {bolde}_{k - 1}^{*} false(i + 1, j + 1 false)}{μ + {boldΨ}_{k - 1} {(i, j)}^{T} {boldΨ}_{k - 1} false(i, j false)} {boldΨ}_{k - 1} {(i, j)}^{T}

where η > 0 is a step‐size constant and μ is a positive weighting factor.Remark Different from the traditional AILC methods for repetitive 1D time‐dynamic systems, 24‐30,37 both the learning controller (9) and the iterative estimator (10) of the proposed 2D‐AILC are conducted iteratively with 2D‐dynamic evolution, which makes the convergence analysis more difficult. Remark Different from the AILC methods for 2D dynamic systems, 23 the proposed 2D‐AILC approach not only considers both the iteration‐varying desired references and the nonuniform trial lengths but also does not need the identical initial conditions. And thus, it is a significant extension of the previous work to enhance the applicability in real‐world industries.…”

Section: Two‐dimensional Ailc With Variant Trial Lengthsmentioning

confidence: 99%

“…In contrast, rare works 21‐23 have been reported for the ILC problem of the 2‐D systems that repeat over a finite duration. Further, a fundamental requirement in References 21‐23 is the strictly repetitive conditions, including identical initial states, identical desired trajectory, repeatable disturbances, identical trial lengths, and so on. If there are any iteration‐dependent changes, the convergence may no longer be guaranteed and the learning action has to restart from the beginning.…”

Section: Introductionmentioning

confidence: 98%

“…Recently, many control methods have emerged for 2‐D systems, such as H ∞ control, 16,17 optimal guaranteed cost control, 18,19 and sliding mode control 20 . In contrast, rare works 21‐23 have been reported for the ILC problem of the 2‐D systems that repeat over a finite duration. Further, a fundamental requirement in References 21‐23 is the strictly repetitive conditions, including identical initial states, identical desired trajectory, repeatable disturbances, identical trial lengths, and so on.…”

Section: Introductionmentioning

confidence: 99%

“…However, fewer results have been presented for the AILC method of 2D systems. In Reference 23, an AILC method is discussed for 2D systems with nonrepetitive desired trajectories and random boundary conditions, but the problem of nonuniform trial lengths has not been considered.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive iterative learning control for 2D nonlinear systems with nonrepetitive uncertainties

Xing

Chi

Lin

2020

Intl J Robust & Nonlinear

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This paper explores the iterative learning control (ILC) problem for two‐dimensional (2D) multi‐input multi‐output nonlinear parametric systems by taking all nonrepetitive uncertainties of stochastic initial shifts, different tracking tasks and nonuniform trial lengths into consideration. A 2D stochastic variable is defined with Bernoulli stochastic distribution for the first time to handle iteration‐varying trial lengths. The desired output is incorporated into the learning control law as a feedback to compensate the iterative changes of the tracking tasks. An iterative 2D parameter updating law is established using a new defined virtue tracking error to well address the systems uncertainties and varying trial lengths. Consequently, a novel 2D adaptive ILC (2D‐AILC) is presented by incorporating the control law and parameter updating law. The convergence is proved by introducing both the Lyapunov stability principle and the 2D key technique lemma into the repetitive 2D systems even though the dynamic evolution along with two‐dimensional directions makes it more difficult in the mathematic analysis. The simulation study tests the theoretical results: the presented 2D‐AILC scheme can still accomplish a tracking task exactly even though there exist random initial states, nonrepetitive reference trajectories, and iteration‐varying trial lengths.

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“…The learning control law of the 2D‐AILC for MIMO systems is presented as

{boldu}_{k} false(i, j false) = {\overset{Φ}{true}}_{k} false(i, j false) {boldΨ}_{k} false(i, j false), false(i, j false) \in {boldℤ}_{T_{1 normalk}} \times {boldℤ}_{T_{2 k}}

and the parameter updating law for

{\overset{Φ}{true}}_{k} false(i, j false)

is given as

{\overset{Φ}{true}}_{k} false(i, j false) = {\overset{Φ}{true}}_{k - 1} false(i, j false) + \frac{η {bolde}_{k - 1}^{*} false(i + 1, j + 1 false)}{μ + {boldΨ}_{k - 1} {(i, j)}^{T} {boldΨ}_{k - 1} false(i, j false)} {boldΨ}_{k - 1} {(i, j)}^{T}

Section: Two‐dimensional Ailc With Variant Trial Lengthsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive iterative learning control for 2D nonlinear systems with nonrepetitive uncertainties

Xing

Chi

Lin

2020

Intl J Robust & Nonlinear

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“…In contrast to 1-D dynamical system, the control objective is no longer tracking curve, but surface in 2-D system. Thus, owing to the more complicated tracking task and no direct analysis tool of 2-D dynamical system, the ILC control design of 2-D dynamical system is much more challenging [10]. To date, some authors have devoted themselves to the study of ILC in 2-D dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Design of Adaptive ILC for 2-D FMM Systems With Unknown Control Directions

Wei

Wan

2019

IEEE Access

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Among the existing adaptive iterative learning control (ILC) work concerning unknown control direction problem, no result is available for the two-dimensional (2-D) dynamical systems. In this paper, an adaptive ILC is developed for a class of 2-D dynamical systems described by the Fornasini-Marchesini model (FMM). Notably, the 2-D FMM system under investigation possesses not only random uncertainties in boundary condition and reference trajectory, but also unknown control direction. Even so, the constructed adaptive ILC combining with a modification mechanism can still guarantee the precise tracking of iteration-variant reference trajectory and the boundedness of all the system signals, as iteration number k tends to infinity. Theoretical analysis and simulation study are given to demonstrate the effectiveness of the developed adaptive ILC. INDEX TERMS Two-dimensional (2-D) dynamical systems, unknown control direction, adaptive iterative learning control (ILC), the Fornasini-Marchesini model (FMM).

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Robust decentralized iterative learning control for large‐scale interconnected systems described by 2‐D Fornasini–Marchesini systems with iteration‐dependent uncertainties including boundary states, disturbances, and reference trajectory

Wan

2022

Adaptive Control & Signal

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This article first investigates robust iterative learning control (ILC) problem of a class of large-scale interconnected systems, which consist of many subsystems described by two-dimensional linear discrete first Fornasini-Marchesini systems with iteration-dependent uncertainties arising from not only boundary states, disturbances, but also reference trajectory. A decentralized P-type ILC law without any information exchanges with other subsystems is proposed such that the ultimate ILC tracking error of each subsystem can converge to a bounded range, the bound of which depends continuously on the bounds of all iteration-dependent uncertainties considered. Especially, if these iteration-dependent uncertainties are convergent progressively along the iteration direction, perfect ILC tracking on 2-D reference trajectory can be obtained.Additionally, a modified ILC law with compensation technique is used to a class of large-scale interconnected systems composed of many subsystems represented by two-dimensional linear discrete second Fornasini-Marchesini systems. Two simulation examples are used to demonstrate the effectiveness and validity of the obtained ILC results. Finally, some comparative discussions are given.

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Adaptive ILC for tracking non-repetitive reference trajectory of 2-D FMM under random boundary condition

Cited by 26 publications

References 22 publications

Adaptive iterative learning control for 2D nonlinear systems with nonrepetitive uncertainties

Adaptive iterative learning control for 2D nonlinear systems with nonrepetitive uncertainties

Design of Adaptive ILC for 2-D FMM Systems With Unknown Control Directions

Robust decentralized iterative learning control for large‐scale interconnected systems described by 2‐D Fornasini–Marchesini systems with iteration‐dependent uncertainties including boundary states, disturbances, and reference trajectory

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