Bifurcation Control of chaotic Dynamical Systems

Abstract

A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems. The first of these ideas is the need for robust control, in the sense that, even with an uncertain dynamic model of the system, the design ensures stabilization without at the same time changing the underlying equilibrium structure of the system. Secondly, the paper shows how focusing on the control of primary bifurcations in the model can result in the taming of chaos. The latter is an example of the 'bifurcation control' approach. When employed along with a dynamic feedback approach to the equilibrium structure preservation issue noted above, this results in a family of robust feedback controllers by which one can achieve various types of 'stability' for the system.