# American Institute of Mathematical Sciences

March  2020, 10(1): 39-41. doi: 10.3934/naco.2019031

## 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

Received  July 2018 Revised  April 2019 Published  May 2019

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.

Citation: John T. Betts, Stephen L. Campbell, Claire Digirolamo. Initial guess sensitivity in computational optimal control problems. Numerical Algebra, Control & Optimization, 2020, 10 (1) : 39-41. doi: 10.3934/naco.2019031
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Graphs of computed optimal control $w$ for Example (2) with DT approach and $M = 2, T = 1.$
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
 $i$ $w_0$ $w_f$ 1 1 0 2 -1 -1 3 1 -1 4 0 1
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
 $\gamma^2$ $w_1$ $w_2$ $w_3$ $w_4$ 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
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
 $\gamma^2$ $w_1$ $w_2$ $w_3$ $w_4$ 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
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
 $\gamma^2$ $w_1$ $w_2$ $w_3$ $w_4$ 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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