Kybernetika 50 no. 4, 596-615, 2014

Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria

Hassan Saberi Nik, Ping He and Sayyed Taha TalebianDOI: 10.14736/kyb-2014-4-0596


In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose Lyapunov stability to control the Pehlivan-Uyaroglu system with unknown parameters by way of a feedback control approach and a single controller. Numerical simulations are performed to demonstrate the effectiveness of the proposed control strategies.


optimal control, adaptive control, autonomous chaotic system, single state feedback control, Pontryagin Minimum Principle


34D20, 58E25, 93C10, 37N35


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