𝔖 Bobbio Scriptorium
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On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

✍ Scribed by Marat Rafikov; José Manoel Balthazar

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
264 KB
Volume
13
Category
Article
ISSN
1007-5704

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✦ Synopsis

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Ro ¨ssler system and synchronization of the hyperchaotic Ro ¨ssler system.

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