Composite Dynamical System for Controlling Chaos

Tetsushi UETA  Hiroshi KAWAKAMI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E78-A    No.6    pp.708-714
Publication Date: 1995/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Systems and Control
controlling chaos,  Poincar mapping stabilization,  destabilization,  

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We propose a stabilization method of unstable periodic orbits embedded in a chaotic attractor of continuous-time system by using discrete state feedback controller. The controller is designed systematically by the Poincar mapping and its derivatives. Although the output of the controller is applied periodically to system parameter as small perturbations discontinuously, the controlled orbit accomplishes C0. As the stability of a specific orbit is completely determined by the design of controller, we can also use the method to destabilize a stable periodic orbit. The destabilization method may be effectively applied to escape from a local minimum in various optimization problems. As an example of the stabilization and destabilization, some numerical results of Duffing's equation are illustrated.