Optimal Control of Chaotic Systems

The problem of controlling a chaotic system is treated from a long term statistical basis. Unlike the OGY targeting method that exploits individual unstable orbits, this approach is concerned with targeting the density function of an invariant probability measure. Given a point transformation T, possessing a density function f, we choose , a different probability density function, to be the target. Using optimization methods, we construct a point transformation , close to T, whose invariant probability density function is , or close to .