Browsing by Author "Chen, Hsien-Keng"

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A new study of chaotic behavior and the existence of Feigenbaum's constants in fractional-degree Yin-Yang Henon maps
(2013-10-01)
Ho, Chun-Yen
;
Chen, Hsien-Keng
;
Ge, Zheng-Ming
;
機械工程學系
;
Department of Mechanical Engineering
In this paper, we firstly develop fractional-degree H,non maps with increasing and decreasing argument n. Yin and Yang are two fundamental opposites in Chinese philosophy. Yin represents the moon and is the decreasing, negative, historical, or feminine principle in nature, while Yang represents the sun and is the increasing, positive, contemporary, or masculine principle in nature. Chaos produced by increasing n is called Yang chaos, that by decreasing n Yin chaos, respectively. The simulation results show that chaos appears via positive Lyapunov exponents, bifurcation diagrams, and phase portraits. In order to examine the existence of chaotic behaviors in fractional-degree Yin-Yang H,non maps, Feigenbaum's constants are measured in this paper. It is found that the Feigenbaum's constants in fractional-degree Yin-Yang H,non maps are of great precision to the first and second Feigenbaum's constants. A detailed analysis of the chaotic behaviors is also performed for the fractional-degree H,non maps with increasing (Yang) and decreasing (Yin) argument n.
Chaos synchronization of Yin and Yang T-S fuzzy models of Henon map system
(2013-07-01)
Ho, Chun-Yen
;
Chen, Hsien-Keng
;
Ge, Zheng-Ming
;
機械工程學系
;
Department of Mechanical Engineering
Based on the Chinese philosophy, Yin is the decreasing, negative, historical or feminine principle in nature, while Yang is the increasing, positive, contemporary or masculine principle in nature. Yin and Yang are two fundamental opposites in Chinese philosophy. Since the discrete Henon map system is an invertible map, Yin-Yang T-S fuzzy model of chaotic Henon map systems with increasing and decreasing argument can be studied. The Yang T-S fuzzy model of chaotic Henon map system is presented. The Yin T-S fuzzy model of chaotic Henon map system and Yin T-S fuzzy rules are obtained by invertible matrix in linear system theory. Chaos synchronization of Yang T-S fuzzy model of Henon map systems is achieved by parallel distributed compensation technique, and the fuzzy controller for chaos synchronization of Yin T-S fuzzy model of Henon map systems is also obtained by invertible matrix in linear system theory. The design of the Yin fuzzy controller is fleetly obtained by the inverse of Yang fuzzy controller, the concern is the Yin chaotic system must be an inverse of the Yang chaotic system. T-S fuzzy model scheme is used in the nonlinear discrete chaotic map system, so the nonlinear discrete chaotic map system can be analyzed by linear system theory.
Design of PDC Controllers by Matrix Reversibility for Synchronization of Yin and Yang Chaotic Takagi-Sugeno Fuzzy Henon Maps
(2012)
Ho, Chun-Yen
;
Chen, Hsien-Keng
;
Ge, Zheng-Ming
;
機械工程學系
;
Department of Mechanical Engineering
This paper investigates the synchronization of Yin and Yang chaotic T-S fuzzy Henon maps via PDC controllers. Based on the Chinese philosophy, Yin is the decreasing, negative, historical, or feminine principle in nature, while Yang is the increasing, positive, contemporary, or masculine principle in nature. Yin and Yang are two fundamental opposites in Chinese philosophy. The Henon map is an invertible map; so the Henon maps with increasing and decreasing argument can be called the Yang and Yin Henon maps, respectively. Chaos synchronization of Yin and Yang T-S fuzzy Henon maps is achieved by PDC controllers. The design of PDC controllers is based on the linear invertible matrix theory. The T-S fuzzy model of Yin and Yang Henon maps and the design of PDC controllers are novel, and the simulation results show that the approach is effective.
Pragmatical adaptive synchronization - New fuzzy model of two different and complex chaotic systems by new adaptive control
(2014-09-01)
Li, Shih-Yu
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Chen, Hsien-Keng
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Tam, Lap-Mou
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Huang, Sheng-Chieh
;
Ge, Zheng-Ming
In this paper, (1) a new fuzzy model is presented to simulate two different chaotic systems with different numbers of nonlinear terms and (2) a new adaptive approach and a new control Lyapunov function are proposed to synchronize these two different fuzzy chaotic systems and speed up the convergence of errors. By using this new model, the numbers of fuzzy rules of chaotic systems can be reduced from 2(N) to 2 x N and only 2 subsystems are needed, where N is the number of nonlinear terms. The fuzzy systems become much simpler. In addition, through the new fuzzy model, the new fuzzy systems are much simpler than T-S fuzzy systems (when nonlinear systems are complicated) and can be used to any other kind of application in fuzzy logic control or fuzzy modeling. Mathieu-Van der Pol system (which is called M-V system in this paper) and Quantum cellular neural networks nanosystem (which is called Q-CNN system in this paper) are used for illustrations in numerical simulation results to show the effectiveness and feasibility of our new adaptive approach and new control Lyapunov function. The T-S fuzzy modeling and traditional adaptive control are also given in Appendices B and C for comparison. (C) 2014 Elsevier Inc. All rights reserved.
System Modeling and Synchronization of Nonlinear Chaotic Systems with Uncertainty and Disturbance by Innovative Fuzzy Modeling Strategy
(2013)
Li, Shih-Yu
;
Ko, Li-Wei
;
Lin, Chin-Teng
;
Tam, Lap-Mou
;
Chen, Hsien-Keng
In this paper, an application of the innovative fuzzy model [1] is applied to simulate and synchronize two classical Sprott chaotic systems with unknown noise and disturbance. In traditional Takagi-Sugeno fuzzy (T-S fuzzy) model, there will be 2(N) linear subsystems (according to 2(N) fuzzy rules) and m x 2(N) equations in the T-S fuzzy system, where N is the number of minimum nonlinear terms and m is the order of the system. Through the new fuzzy model, a complicated nonlinear system is linearized to a simple form - linear coupling of only two linear subsystems and the numbers of fuzzy rules can be reduced from 2(N) to 2 x N. The fuzzy equations become much simpler. There are two Sprott systems in numerical simulations to show the effectiveness and feasibility of new model.