| Abstract: |
| Given two local minima of an optimal control problem, can one be deformed into the other by continuously moving the boundary conditions, all the while remaining a local minimum? In other words, is the set of all local minima over all possible boundary conditions path-connected? In this talk, I will describe a sufficient condition for this set to be path-connected that relies on two types of symmetries (invariance under the action of a Lie group and invariance under a rescaling of time). I will then discuss some examples where this set is path-connected, some examples where it is not, and an application in robotics. |
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