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Abstract This paper is concerned with solving, from the learning-based decomposition control viewpoint, the problem of output tracking with nonperiodic tracking–transition switching. Such a nontraditional tracking problem occurs in applications where sessions for tracking a given desired trajectory are alternated with those for transiting the output with given boundary conditions. It is challenging to achieve precision tracking while maintaining smooth tracking–transition switching, as postswitching oscillations can be induced due to the mismatch of the boundary states at the switching instants, and the tracking performance can be limited by the nonminimum-phase (NMP) zeros of the system and effected by factors such as input constraints and external disturbances. Although recently an approach by combining the system-inversion with optimization techniques has been proposed to tackle these challenges, modeling of the system dynamics and complicated online computation are needed, and the controller obtained can be sensitive to model uncertainties. In this work, a learning-based decomposition control technique is developed to overcome these limitations. A dictionary of input–output bases is constructed offline a priori via data-driven iterative learning first. The input–output bases are used online to decompose the desired output in the tracking sessions and design an optimal desired transition trajectory with minimal transition time under input-amplitude constraint. Finally, the control input is synthesized based on the superpositioning principle and further optimized online to account for system variations and external disturbance. The proposed approach is illustrated through a nanopositioning control experiment on a piezoelectric actuator.
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Combining Learning and Model Based Multivariable Control
Artificial neural networks have traditionally been used to implement machine learning algorithms. There are, however, alternatives to these biologically inspired machine learning architectures that offer potentially lower complexity and stronger theoretical underpinnings. One such option in the context of control is based on using a generic input-output model known as a Chen-Fliess functional series. The main goal of the paper is to describe a specific architecture that can be used in the multivariable setting to combine both learning and model based control. It builds on recent work by the authors showing that a certain monoid structure underlies any recursive implementation of such a system. The method is demonstrated using a two-input, two-output Lotka-Volterra system.
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- PAR ID:
- 10205574
- Date Published:
- Journal Name:
- Proc. 58th IEEE Conference on Decision and Control
- Page Range / eLocation ID:
- 1013 - 1018
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC40024.2019.9028944
