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Chaotic Dynamics and Control of Systems and Processes in by G. Rega, F. Vestroni

By G. Rega, F. Vestroni

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13] C. Wu, Y. Yang, and L. Chua, “On adaptive synchronisation and control of nonlinear dynamical systems,” Intern. J. of Bifurcation and Chaos, 6, pp. 455–471, 1996. [14] S. S. Ge and C. Wang, “Adaptive control of uncertain Chua circuits,” IEEE Trans. on Circuit and Systems-I, 47, 9, pp. 1397–1402, 2000. [15] H. Huijberts, H. Nijmeijer, and R. Willems, “System identification in communication with chaotic systems,” IEEE Trans. on Circuit and Systems-I, 47, 6, pp. 800–808, 2000. [16] A. L. Fradkov, V.

10) Hence, according to previous discussion, signal / is bounded and signal &/ is ultimately bounded. Let us analyze the following Lyapunov function    candidate with respect to part of variables [21] : (  )= γ − (  −  ) (  −  ) , its time derivative for system (8) takes form: 7 : = −  ( −  ) ≤− &  7  − 7  7  ( ( −  ))≤ & & /+ + &/ = − γ & : + & /     According to Lemma 1 solution of the last linear time-varying inequality is bounded, if functions γ & ( W )  and &/( W )  are.

This speculative model may provide a paradigm for the role of nonlinear dynamics and chaotic noise in the design evolution of machines. 5. References [1] H. G. Conway, “Origins of mechanical servo mechanisms”, The Newcomen Society, Vol. XXIX, 1953-54, 1954-55. [2] F. C. Moon, Chaotic and Fractal Dynamics, J. Wiley, New York, 1992. [3] F. Reuleaux, The Constructor, 4th Edition, Translated by H. Suplee, 1893. [4] C. Huygens, Horologium, 1658. [5] D. Sobel and W. J. H. Y, 1998. [6] G. B. Airy, (1826) “On the disturbances of pendulums and balances and the theory of escapements”, Trans.

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