Initial guess sensitivity in computational optimal control problems

John T. Betts; Stephen L. Campbell; Claire Digirolamo

doi:10.3934/naco.2019031

Article Contents

2020, Volume 10, Issue 1: 39-43. Doi: 10.3934/naco.2019031

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Initial guess sensitivity in computational optimal control problems

1.
Applied Mathematical Analysis, 24748 SE Mirromont Pl., Issaquah, WA 98027, USA
2.
Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA

^* Corresponding author: Stephen L Campbell
^* Corresponding author: Stephen L Campbell

Received: July 2018

Revised: April 2019

Published: March 2020

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Abstract

An optimal control problem is presented that exhibited unexpected initial guess dependence when being solved with direct transcription methods. This note presents that example and the cautionary tale it provides.

Keywords:

Mathematics Subject Classification: Primary: 49M37; Secondary: 49K40, 49M25.

Citation:

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Figure 1. Graphs of computed optimal control $ w $ for Example (2) with DT approach and $ M = 2, T = 1. $

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Table 1. Endpoints for Initial $ w $ guesses $ w_i $ for Example 2

$ i $	$ w_0 $	$ w_f $
1	1	0
2	-1	-1
3	1	-1
4	0	1

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Table 2. Adjusted Values of $ \eta(T) $ for Example (2) using DT and $ M = 2 $, $ T = 1 $ and 3 iterations for different values of $ \gamma^2 $ and $ w_i $

$ \gamma^2 $	$ w_1 $	$ w_2 $	$ w_3 $	$ w_4 $
4.3	18.0613	5.3457	18.0613	18.0613
4.4	18.0613	5.3457	18.0613	5.3457
4.5	18.0613	18.0613	5.3457	5.3457
4.6	18.0613	18.0613	18.0613	18.0613
4.7	5.3457	5.3457	18.0613	5.3457

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Table 3. Rerun of the results reported in Table Table 2. Bold entries have changed from Table 2

$ \gamma^2 $	$ w_1 $	$ w_2 $	$ w_3 $	$ w_4 $
4.3	18.0613	5.3457	18.0613	18.0613
4.4	18.0613	5.3457	18.0613	5.3457
4.5	18.0613	18.0613	5.3457	5.3457
4.6	5.3457	18.0613	5.3457	18.0613
4.7	5.3457	5.3457	18.0613	5.3457

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Table 4. Adjusted Values of $ \eta(T) $ for Example (2) using DT and $ M = 2 $, $ T = 1 $ and 3 iterations for cost (3)

$ \gamma^2 $	$ w_1 $	$ w_2 $	$ w_3 $	$ w_4 $
4.3	18.0613	18.0613	5.3457	18.0613
4.4	18.0613	18.0613	5.3457	5.3457
4.5	18.0613	18.0613	5.3457	18.0613
4.6	18.0613	18.0613	5.3457	18.0613
4.7	18.0613	18.0613	5.3457	5.3457

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References

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