Control and stabilization of systems with homoclinic orbits

Bloch, A. M. and J. E. Marsden

In Proceedings of the 28th IEEE Conference on Decision and Control, IEEE, New York, 1-3, (1989), 2238-2242

Abstract:

In this paper we consider 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. In the fluid system we show how the structure of the phase space can be used to keep the system near an (unstable) saddle. For the rigid body system we discuss passage along the orbit as a possible control maneuver, and shoe how the Energy-Casimir method can be used to analyze stabilization of the system about the saddles.