Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

Deyuan Meng; Jingyao Zhang

doi:10.1109/JAS.2021.1003973

Volume 8 Issue 5

May 2021

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2021 > 8(5): 1001-1014

D. Y. Meng, J. Y. Zhang, "Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties," IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 1001-1014, May. 2021. doi: 10.1109/JAS.2021.1003973

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D. Y. Meng, J. Y. Zhang, "Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties," IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 1001-1014, May. 2021. doi: 10.1109/JAS.2021.1003973

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Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

doi: 10.1109/JAS.2021.1003973

Deyuan Meng^{1, 2
,
,},
Jingyao Zhang^{1, 2
,}

1.
Seventh Research Division, Beihang University (BUAA), Beijing 100191, China
2.
School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing 100191, China

Funds: This work was supported by the National Natural Science Foundation of China (61873013, 61922007)

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Abstract

Abstract

This paper aims to solve the robust iterative learning control (ILC) problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties. A new optimization-based method is proposed to design and analyze adaptive ILC, for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices. It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC, where the boundedness of system trajectories and estimated parameters can be ensured, regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties. Two simulation tests, especially implemented for an injection molding process, demonstrate the effectiveness of our robust optimization-based ILC results.
- Adaptive iterative learning control (ILC),
- nonlinear time-varying system,
- robust convergence,
- substochastic matrix

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References

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We address the robust iterative learning control (ILC) problem for nonlinear time-varying systems in the presence of nonrepetitive uncertainties. We propose a new optimization-based design method for adaptive ILC. This new design method makes it feasible to directly apply the contraction mapping-based analysis approach of ILC to develop the boundedness of estimated parameters that are used in our adaptive updating law for the estimation of unknown time-varying nonlinearities.
We introduce a new robust convergence analysis method for optimization-based adaptive ILC by implementing a double-dynamics analysis approach and resorting to the use of the properties of the substochastic matrices. This makes it possible to not only accomplish the robust convergence analysis of optimization-based adaptive ILC, but also guarantee the boundedness of all the system trajectories.
Our design methods and analysis results of optimization-based adaptive ILC can effectively work, regardless of the presence of nonrepetitive uncertainties. This particularly helps to overcome the drawbacks of those methods and results for optimization-based adaptive ILC established through applying the eigenvalue-based contraction mapping approach.

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

doi: 10.1109/JAS.2021.1003973

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