Journal of Advanced Research in Name Vol. 00 No. 0, pp. 1-24 January 2014 Optimization of the synchronization of the mod- ified Duffing system Michaux Kountchou Noube 1 , Patrick Louodop 1 , Samuel Bowong 2, ∗ , Hilaire Fotsin 1 1 Laboratory of Electronics, Automation and Signal Processing, University of Dschang, PO Box 67 Dschang, Cameroon. 2 Department of Mathematics and Computer Science, University of Douala, PO Box 24157 Douala, Cameroon. Abstract. This paper addresses the problem of optimization of the synchronization of a modified Duffing system. We first propose a new four-dimensional autonomous system obtained by the modification of the classical two-dimensional Duffing sys- tem. The dynamical behaviors of the modified system are investigated. Furthermore, we propose a robust feedback coupling which accomplishes the synchronization of two modified chaotic systems using an optimal tuning scheme based on the Riccatti equation. The approach developed considers incomplete state measurements and no detailed model of the system to guarantee the robust stability. This approach includes an uncertainty estimator and leads to a robust feedback coupling. A finite horizon can be arbitrarily established to ensure that the chaos synchronization is achieved at established time. An advantage is that the proposed scheme accounts the energy wasted by the controller and the closed-loop performance on synchronization. Both stability analysis and numerical simulations are presented to show the effectiveness of the proposed optimization strategy. Pspice analog circuit implementation of the com- plete master-slave-controller system is presented to show the practical applicability of the proposed scheme. Keywords: Modified Duffing system, Synchronization, Optimization, Ricatti Equation, Pspice simulation. Mathematics Subject Classification 2010: 20N15, 20C99. * Correspondence to: Samuel Bowong, Department of Mathematics and Computer Science, University of Douala, PO Box 24157 Douala, Cameroon. Email: sbowong@gmail.com * Received: 3 october 2009 http://www.i-asr.com/Journals/ 1 c ⃝2010 Institute of Advanced Scientific Research