Control and stabilization of systems with homoclinic orbits

Consideration is given to the control of two physical systems, the near wall region of a turbulent boundary layer and the rigid body, using techniques from the theory of nonlinear dynamical systems. Both these systems have saddle points linked by heteroclinic orbits. It is shown how, in the fluid system, the structure of the phase space can be used to keep the system near an (unstable) saddle point. For the rigid body system, passage along the orbit is discussed as a possible control maneuver, and it is shown how the energy-Casimir method can be used to analyze stabilization of the system about the saddle points