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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Sparse Sensing and Optimal Precision: Robust H∞ Optimal Observer Design with Model Uncertainty
We present a framework which incorporates three aspects of the estimation problem, namely, sparse sensor con- figuration, optimal precision, and robustness in the presence of model uncertainty. The problem is formulated in the H∞ optimal observer design framework. We consider two types of uncertainties in the system, i.e. structured affine and un- structured uncertainties. The objective is to design an observer with a given H∞ performance index with minimal number of sensors and minimal precision values, while guaranteeing the performance for all admissible uncertainties. The problem is posed as a convex optimization problem subject to linear matrix inequalities. Numerical simulations demonstrate the application of the theoretical results presented in this work.
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- Award ID(s):
- 1762825
- NSF-PAR ID:
- 10288122
- Date Published:
- Journal Name:
- American Control Conference
- Page Range / eLocation ID:
- 4105 to 4110
- 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/10.23919/ACC50511.2021.9483378
