By G. Rega, F. Vestroni
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The addition of the extra state variable and the coupling matrix A has two effects on the map dynamics; the first is to change the width of the PDF of the map around the cycle-two points. The second effect is to increase the separation between the two fixed points. A plot of these two measures of performance (Figure 6) shows that the complex ‘machine’ {A and ε } can produce a minimum in the noise induced PDF of the dynamics. Thus the added complexity of the ‘machine’ can optimize the dynamic performance.
V. Voronov, “Adaptive backstepping with high-order tuner,” Automatica, 37, pp. 1953 – 1960, 2001. [19] F. Moon, Chaotic and Fractal Dynamics. An Introduction for Applied Scientists and Engineers. Wiley, 1992. [20] G. Nikolis and I. R. Prigogine, Self-Organization in Non-Equilibrium Systems. Wiley, New York, 1977. V. S. Oziraner, Stability and stabilization of motion with respect to part of variables. Moscow, Nauka. P. 263, 1987, (in Russian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± © 2005 Springer.
Marino, “Adaptive observers for single output nonlinear systems,’ IEEE Trans. Aut. , AC–35, pp. 1054 – 1058, 1990. [11] A. Yu. Markov and A. L. Fradkov, “Adaptive synchronisation of coupled chaotic systems,” Proc. Int. Conf. "Fractals and Chaos in Chemical Engineering", Rome, Sept. 2–5, pp. 153–154, 1996. [12] H. Nijmeijer and I. M. Y. Mareels, “An observer looks at synchronization,” IEEE Trans. on Circuit and Systems-I, 44, 10, pp. 882–890, 1997. [13] C. Wu, Y. Yang, and L. Chua, “On adaptive synchronisation and control of nonlinear dynamical systems,” Intern.