### Roger Brockett, *Harvard*

### Optimal Cyclic Processes and subRiemannian Geodesics

The basic mechanisms involved in wide variety of engineering and biological processes depend on properties of non integrable distributions define by collections of vector fields. It often happens that the most efficient trajectories define closed subriemannian geodesics. In this talk we will establish some of the more remarkable properties of such trajectories, with emphasis on some especially tractable situations in which the manifold admits the structure of a Riemann symmetric space with the subriemannian structure being “matched” to the structure of the symmetric space in an obvious way. We also show that the geodesic sphere associated with these problems can not be differentiable and discuss the relationship between this fact and feedback stabilization.

Seminar is in **Altgeld Hall 345**, on ** Mondays 1:30pm**.

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