Risk-aware optimal policy/value function movies

Here we provide supplemental movies showing how optimal steering/switching feedback policies evolve (for both tacks simultaneously) from the maximum \(s = \bar{s}\) to \(s = 0\) in a decreasing order.

  • As in the main text, for the optimal policy plot: Colors indicate the optimal steering angle \(u_*\) in the current tack, while the complement (left blank) shows all the (\(r, \theta \)) configurations at which the immediate tack-switch is optimal.
  • All examples are computed on a \(1601 \times 1601 \times 2\) uniform grid in the \(r, \theta, q\)-space with \(\Delta s = 0.025\)

Moives:

The follownig 4 movies all show contour plots in the relative (\(r, \theta \))-space where within each frame:

    \( a = 0 \) and \( \sigma = 0.05 \) (\( \bar{s} = 70 \)):
    \( a = 0.15 \) and \( \sigma = 0.05 \) (\( \bar{s} = 55 \)):
    \( a = 0.05 \) and \( \sigma = 0.05 \) (\( \bar{s} = 55 \)):
    \( a = 0.05 \) and \( \sigma = 0.1 \) (\( \bar{s} = 55 \)):

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