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Published in:
2022 | OriginalPaper | Chapter
3. Control of Nonhyperbolic Dynamical Systems Through Center Manifold Control
Author : Firdaus E. Udwadia
Published in: Nonlinear Approaches in Engineering Application
Publisher: Springer International Publishing
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Abstract
This chapter proposes a simple approach for the control of nonlinear dynamical systems with nonhyperbolic equilibrium points. Such equilibrium points are generally much more difficult to analyze dynamically, and correspondingly the control of nonlinear systems in the vicinity of such points can often become more difficult. The aim is to bring about asymptotically stable behavior of the controlled system in the vicinity of the nonhyperbolic equilibrium point. A new way to control such systems is proposed here through control of their local center manifolds. A simple and effective methodology for doing this is provided, and its advantages are illustrated through several examples.