Seminar Details
2012-12-04 (14.00) : A deterministic optimal control problem with a chaotic solution
At Euler building
Organized by Mathematical Engineering
Speaker :
Roland Hildebrand (CESAME)
Abstract :
It is well-known that in continuous-time dynamical systems of dimension greater or equal than 3 chaotic behaviour can occur. Perhaps the most simple, but rather typical example is Smale's Horseshoe, which appears whenever the stable and unstable submanifolds of a hyperbolic fixed point of the two-dimensional Poincare return map in the neighbourhood of a periodic trajectory intersect in a second point.
We present a 4-dimensional, linear-quadratic, deterministic optimal control problem whose optimal solution exhibits a dynamics emanating from a Smale's Horseshoe. Chaotic behaviour was previously not known to occur in optimal control problems.
This is joint work with M.I. Zelikin and L.V. Lokutsievski (Moscow State University).