By Bingo Wing-Kuen Ling, Herbert Ho-Ching Iu, Hak-Keung Lam
During this e-book, top researchers current their present paintings within the demanding region of chaos keep watch over in nonlinear circuits and platforms, with emphasis on sensible methodologies, procedure layout thoughts and purposes. a mix of evaluation, instructional and technical articles, the e-book describes state of the art study on major difficulties during this sector. The scope and goal of this booklet are to bridge the space among chaos keep an eye on equipment and circuits and platforms. it's an excellent place to begin for somebody who wishes a primary knowing of controlling chaos in nonlinear circuits and platforms.
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Extra resources for Control of chaos in nonlinear circuits and systems
Example text
2. System state responses of the response Rössler system with u(t) = 0 for 0 ≤ t < 50s and the switching controller applied for t ≥ 50s. K. F. Leung e1(t) 50 0 -50 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 Time (sec) 70 80 90 100 e2(t) 50 0 -50 60 e3(t) 40 20 0 -20 Fig. 3. The tracking error of the response Rössler to the drive Lorenz chaotic systems. tracking error is shown in Fig. 3. Referring to these figures, it can be seen that the proposed switching controller, which is applied for t ≥ 50s, is able to drive the system states of the uncertain Rössler system to follow those of the uncertain Lorenz system with a sufficiently small tracking error.
Comparing to the chaos stabilization problem, chaos synchronization is much harder to be achieved. To stabilize the chaos behaviour, the control objective is only to suppress the chaotic dynamics and drive the system states to the equilibrium. However, chaos synchronization requires driving the system states of the response chaotic system to follow those of the drive chaotic system. In such a case, the tracking control problem is considered. Furthermore, the synchronization problem will become more complex if the chaotic systems are subject to parameter uncertainties.
Chua, Robust synthesis for masterslave synchronization of Lur’e systems, IEEE Trans. Circuits Syst. -I 46, 841-850, (1999). [15] J. A. K. Suykens, P. F. Curran, J. Vandewalle, and L. O. Chua, Robust nonlinear H∞ synchronization of chaotic Lur’e systems, IEEE Trans. Circuits Syst. -I 44, 891-904, (1997a). [16] J. A. K. Suykens, J. Vandewalle, and L. O. Chua, Nonlinear H∞ synchronization of chaotic Lur’e systems, Int. J. Bifurcation and Chaos 7, 1323-1335, (1997b). [17] J. A. K. Suykens, P. F. Curran, T.
