Iterative learning control with incomplete information: a survey

Shen, Dong

doi:10.1109/jas.2018.7511123

Cited by 119 publications

(45 citation statements)

References 98 publications

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“…1 Attracted by the significant convergence result that the asymptotical convergence condition is irrelevant to the system state matrix, numerous ILCs have been specified on the basis of the proportional-integral-derivative (PID)-type profile as surveyed in literatures. [2][3][4][5][6] By dedicated devotion, one found that the order of the compensating tracking errors, which is the highest derivative order of the tracking error in the ILC laws for continuous-time systems, play an important role for a system with higher relative degree that is defined as the minimal derivative order of the system output fed by the control input in an explicit form. [7][8][9][10][11][12] For the regard, the rth and the (r − 1)th-order ILCs have been well-constructed for a system with higher relative degree.…”

Section: Introductionmentioning

confidence: 99%

Monotonic convergence and robustness of higher‐order gain‐adaptive iterative learning control

Ruan

2020

Intl J Robust & Nonlinear

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For a class of repetitive linear discrete time-invariant systems with higher relative degree, a higher-order gain-adaptive iterative learning control (HOGAILC) is developed while minimizing the energy increment of two adjacent tracking errors with the argument being the iteration-time-variable learning-gain vector (ITVLGV). By taking advantage of rows/columns exchanging transformation of matrix, the ITVLGV is achieved in an explicit form which is dependent upon the system Markov parameters and adaptive to the iterationwise tracking-error vector. Algebraic derivation demonstrates that the HOGAILC is strictly monotonously convergent. On the basis of the adaptive mode, a damping quasi-HOGAILC strategy is exploited while the uncertainties of the system Markov parameters exist. Rigorous analysis delivers that the damping quasi-scheme is strictly monotonically convergent and thus the HOGAILC mechanism is robust to a wider range of uncertainty of system parameters and the damping factor may relax the uncertainty range. Numerical simulations are made to illustrate the validity and the effectiveness. K E Y W O R D Sdamping factor, gain-adaptive iterative learning control, higher relative degree, iteration-time-variable learning-gain vector, strictly monotonic convergence, uncertainty 1 3960

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Section: Introductionmentioning

confidence: 99%

Monotonic convergence and robustness of higher‐order gain‐adaptive iterative learning control

Ruan

2020

Intl J Robust & Nonlinear

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“…Over the past three decades, ILC has made great progress. [1][2][3][4][5][6] In addition, due to its simple but effective structure, in a practical environment, permanent magnet step motors, 7 high-speed rail train, 8 and robotic-assisted biomedical system 9 use ILC to resolve the corresponding questions.…”

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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“…Since the iterative learning control (ILC) has been invented three decades before, it has been acknowledged as an efficacious intelligent strategy for a robot manipulator to repetitively execute a desired trajectory tracking over a finite time interval [1][2][3]. The mechanism is iterative generating an upgrading control input for the next iteration by means of compensating the control input at the current iteration with its proportional, integral, and/or derivative tracking discrepancy between the current output and the desired trajectory [4][5][6][7][8][9][10][11][12]. The pursuing aim is that the generated control input may drive the system to track the desired trajectory as precise as possible as the iteration index goes on, or in other words, the ILC is convergent.…”

Section: Introductionmentioning

confidence: 99%

Discrete Fourier transform based frequency characteristics of iterative learning control for linear discrete-time systems

Ruan

2019

Adv Differ Equ

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For discrete-time iterative learning control systems, the discrete Fourier transform (DFT) is a powerful technique for frequency analysis, and Toeplitz matrices are a typical tool for the system input-output transmission. This paper first exploits z-transform and DFT-based frequency properties for iterative learning control systems and studies the convergence property of a Toeplitz matrix to the power of iteration index. The exploitation exhibits that for the finite-length discrete-time iterative learning control systems, the time-domain convolution theorem for the z-transform and DFT is no longer true, and the Toeplitz matrix to the power of iteration index converges if and only if the identical diagonal element lies in the unit circle. Then, by considering the DFT to a finite-length sequence as a linear transform, it is easy to equivalently reform the input-output equation of linear discrete time-invariant and time-varying ILC systems as an algebraic discrete-frequency equation. Thus the derivative-type (D-type) iterative learning control (ILC) converges in a discrete-frequency domain if and only if it converges in a discrete-time domain. Numerical simulations are carried out to exhibit the validity and effectiveness.

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Iterative learning control with incomplete information: a survey

Cited by 119 publications

References 98 publications

Monotonic convergence and robustness of higher‐order gain‐adaptive iterative learning control

Monotonic convergence and robustness of higher‐order gain‐adaptive iterative learning control

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

Discrete Fourier transform based frequency characteristics of iterative learning control for linear discrete-time systems

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