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# Initial guess sensitivity in computational optimal control problems

• * Corresponding author: Stephen L Campbell
• 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.

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

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

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

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

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

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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Tables(4)

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