This paper is focused on the output tracking
control problem of a wave equation with both matched and
unmatched boundary uncertainties. An adaptive boundary
feedback control scheme is proposed by utilizing radial basis
function neural networks (RBF NNs) to deal with the effect of
system uncertainties. Specifically, two RBF NN models are first
developed to approximate the matched and unmatched system
uncertain dynamics respectively. Based on this, an adaptive NN
control scheme is derived, which consists of: (i) an adaptive
boundary feedback controller embedded by the NN model
approximating the matched uncertainty, for rendering stable
and accurate tracking control; and (ii) a reference model
embedded by the NN model approximating the unmatched
uncertainty, for generating a prescribed reference trajectory.
Rigorous analysis is performed using the Lyapunov theory
and the C0-semigroup theory to prove that our proposed
control scheme can guarantee closed-loop stability and wellposedness.
Simulation study has been conducted to demonstrate
effectiveness of the proposed approach.
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Data-Driven Decomposition Control to Output Tracking With Nonperiodic Tracking–Transition Switching Under Input Constraint
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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- NSF-PAR ID:
- 10324422
- Date Published:
- Journal Name:
- Journal of Dynamic Systems, Measurement, and Control
- Volume:
- 144
- Issue:
- 6
- ISSN:
- 0022-0434
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4053763
