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The objective of this paper is to develop an open loop insulin input profile over a span of 24 hours which makes the glucose trajectory of a Type 1 diabetic person track a target glucose trajectory. The Bergman minimal model is chosen to represent the glucose-insulin dynamics which is shown to be differentially flat. An optimal control problem is posed by parameterizing the differentially flat output of the Bergman model using Fourier series, to result in an input profile that can be repeatedly administered every day. The solution to the optimization problem is then shown to present acceptable performance in terms of tracking and adhering to imposed constraints.
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Flat Outputs in Terms of SISO Operator Compositions
The goal of this paper is to use a flat coordinate system to show that a flat output for a SISO flat system can be written in terms of a certain composition of input-output operators. The work is partially motivated by the author’s recent work on computing the relative degree of interconnected systems. First the general smooth case is considered, followed by the control affine analytic case. The latter is more amenable to computations in terms of Chen-Fliess series.
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- Award ID(s):
- 1839378
- PAR ID:
- 10205573
- Date Published:
- Journal Name:
- Proc. 58th IEEE Conference on Decision and Control
- Page Range / eLocation ID:
- 8036 - 8041
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC40024.2019.9028949
