Control of chaos in nonlinear circuits and systems by Bingo Wing-Kuen Ling, Herbert Ho-Ching Iu, Hak-Keung Lam

By Bingo Wing-Kuen Ling, Herbert Ho-Ching Iu, Hak-Keung Lam

During this booklet, best researchers current their present paintings within the not easy sector of chaos regulate in nonlinear circuits and platforms, with emphasis on functional methodologies, procedure layout ideas and functions. a mixture of evaluate, instructional and technical articles, the e-book describes state of the art study on major difficulties during this region. The scope and goal of this ebook are to bridge the distance among chaos regulate tools and circuits and structures. it's an incredible start line for someone who wishes a basic knowing of controlling chaos in nonlinear circuits and platforms.

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1. Fig. 4 shows the system state responses with the proposed switching controller using a saturation function with T = 10−5 subject to T the initial state condition of x(0) = [− 1 − 1 − 1] . In this simulation, u(t) = 0 is employed for 0 ≤ t < 50s and the switching controller is applied for t ≥ 50s. The tracking error is shown in Fig. 5. It can be seen from these figures that the proposed switching controller applied for 51 Synchronization of Uncertain Chaotic Systems t ≥ 50s is able to drive the system states of the uncertain Chua’s system to follow those of the uncertain Lorenz system with a sufficiently small tracking error.

The fuzzy model gives a fixed framework to model some general chaotic systems. This particular structure is in favour of the system analysis and controller synthesis. Adaptability was granted to controllers [8, 9] of which the controller parameters were updated in an online manner according to some adaptive laws to cope with the changes of the operating conditions. Consequently, the adaptive controller offered an outstanding robustness property. However, the complex adaptive laws will always increase the computational demand and structural complexity of the fuzzy controllers.

4) is a nonlinear function of x(t) and µ M i ( xα (t )) is the grade of α membership corresponding to the fuzzy terms M αi . It should be noted that the grades of membership, µ M i ( xα (t )) , are uncertain in value as the α chaotic system is subject to parameter uncertainties. 1) but without the control input. 5) j =1 where xˆ (t ) ∈ ℜn×1 is the system state vector. ˆ ∈ ℜ n × n is a known A j constant system matrix; wˆ j (xˆ (t )) ∈ [0 1] is the grade of the q membership and ∑ wˆ j (xˆ (t )) = 1 .

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