Controlling the Dynamics of a Random System

Random systems, dynamical systems and control systems can all be described as flows on (finite or infinite dimensional) spaces, which allows for the use of unified concepts in the analysis of their qualitative long term behavior. In particular there is a close connection between the attractors of an undisturbed system, the stationary and ergodic solutions of the system under Markovian parameter noise, the invariant control sets of an associated control system, and the (chaotic) attractors of the corresponding control flow. This correspondence is used to analyze the possible changes in the ergodic behavior of controlled random nonlinear systems. Discussing four examples in some detail reveals a link to stochastic bifurcation theory.