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

By G. Rega, F. Vestroni

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Due to the complete integrability of the reduced Hamiltonian system, the phase plane behavior provided the whole picture of dynamics, including the homoclinic and heteroclinic invariant manifolds. Melnikov analysis then showed that saddle connections in the reduced phase space are most susceptible and lead to chaotic motions under perturbation. Thus, Hamiltonian dynamics can form a basis for global dynamic analysis. K. Bajaj, A. Vyas and A. 0 -4. 0. -2. 12 = 0 σb 2. 4. 0 -4. -2. 0. σb 2. 0 a2 4.

At the same time, an optimization principle must be established to assign parameters to the new model so that some cost function or performance measure is minimized or maximized to improve 12 Francis C. Moon some aspect of the dynamical behavior. This optimization model differs from classical techniques that often are applied to a fixed dimensional state space. (Haug and Arora, [19]) In our problem however the dimension of the state space grows as the complexity of the machine evolves. For simplicity and to illustrate the methodology we chose a discrete time or iterated map for the clock.

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