Electrical Engineering-Systems Dept.

סמינר מחלקתי

You are invited to attend a lecture by

Dr. Ronald Hildebrand

(University Grenoble, France)

on the subject:

An deterministic optimal control problem with a horseshoe dynamics

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 similar to 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).