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Optimal Control with Signal-Dependent Noise and Endpoint Constraint

Explore learning theory concepts in open-loop optimal control with signal-dependent noise, minimizing position variance, and endpoint constraints. Solve equations with Lagrange multipliers to achieve optimal control strategies.

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Optimal Control with Signal-Dependent Noise and Endpoint Constraint

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  1. 580.691 Learning Theory Reza Shadmehr Open loop optimal control with signal dependent noise and endpoint constraint Minimum endpoint variance with Lagrange multipliers

  2. Minimize position variance at last time point with the constraint that all states are at the goal P equations p+3 unknowns 3 equations p+3 unknowns

  3. Minimize position variance at time p with the constraint that position is maintained at goal for an additional k time points.

  4. Minimize position variance at time p+k with the constraint that position is maintained at goal for k time points.

  5. Minimize sum of position variance over hold period with the constraint that all states are at the goal at first point in hold period.

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