Takagi-Sugeno fuzzy logic controller for Liu-Chen four-scroll chaotic system

Chaos modelling, chaos control and chaos synchronisation are active areas in chaos theory, while research in these areas has potential applications in many fields like nonlinear optics, oscillations, chemical reactions, biology, neurology, secure data encryption, secure communications, robotics, neural networks, fractals and nonlinear circuits design. Especially, chaos control is an important research area, and it has a wide range of applications like control of turbulence, dynamics of lasers, plasma, chemical reactions such as Belousov-Zhabotinsky reaction, ecological systems and cardiac arrhythmias. Until now, many methods for chaos control such as open-loop control based on periodic system excitation, closed-loop control such as OGY method and time-delayed feedback control such as Pyragas method have been used. In this paper, a fuzzy logic control using fuzzy sets and fuzzy logic for the control of chaotic systems has been proposed. In more detail, this work presents a fuzzy logic controller design of a chaotic system using Takagi-Sugeno fuzzy model. The stability analysis of the fuzzy logic controller system is carried out using Barbashin-Krasovskii theorem. For the proposed fuzzy logic control, the Liu-Chen four-scroll chaotic system was used. Finally, the simulation results of the proposed control method present the effectiveness of this method.

[1]  S. Vaidyanathan.  A 3 - D Novel Highly Chaotic System with Four Quadratic Nonlinearities, its Adaptive Control and Anti - Synchronization with Unknown Parameters , 2015 .

[2]  Hua O. Wang,et al.  Fuzzy modeling and control of chaotic systems , 1996 .

[3]  Sundarapandian Vaidyanathan,et al.  Hybrid Synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan Chaotic Systems , 2015, Advances and Applications in Sliding Mode Control Systems.

[4]  Zhongkui Sun,et al.  Inducing or suppressing chaos in a double-well Duffing oscillator by time delay feedback , 2006 .

[5]  Sundarapandian Vaidyanathan,et al.  Adaptive Synchronization of Chemical Chaotic Reactors , 2015 .

[6]  Sundarapandian Vaidyanathan,et al.  Anti-synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan-Madhavan Chaotic Systems , 2015, Advances and Applications in Sliding Mode Control Systems.

[7]  Ioannis M. Kyprianidis,et al.  A chaotic path planning generator for autonomous mobile robots , 2012, Robotics Auton. Syst..

[8]  Ahmad Taher Azar,et al.  Design and Modeling of Anti Wind Up PID Controllers , 2015, Complex System Modelling and Control Through Intelligent Soft Computations.

[9]  Julyan H. E. Cartwright,et al.  Fuzzy Control of Chaos , 1998 .

[10]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[11]  Sundarapandian Vaidyanathan,et al.  Design and SPICE implementation of a 12-term novel hyperchaotic system and its synchronisation via active control , 2015, Int. J. Model. Identif. Control..

[12]  Kestutis Pyragas.  Continuous control of chaos by self-controlling feedback , 1992 .

[13]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[14]  Antonio Mecozzi,et al.  Periodic locking of chaos in semiconductor lasers with optical feedback , 2009 .

[15]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[16]  Sundarapandian Vaidyanathan,et al.  Analysis, Control, Synchronization and SPICE Implementation of a Novel 4 - D Hyperchaotic Rikitake Dynamo System without Equilibrium , 2015 .

[17]  Janusz A. Hołyst,et al.  Chaos control in economical model by time-delayed feedback method , 2000 .

[18]  Sundarapandian Vaidyanathan.  Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities , 2014, Int. J. Model. Identif. Control..

[19]  Radu-Emil Precup,et al.  Lorenz System Stabilization Using Fuzzy Controllers , 2007, Int. J. Comput. Commun. Control.

[20]  Sundarapandian Vaidyanathan,et al.  Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity , 2015, Int. J. Model. Identif. Control..

[21]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[22]  Sundarapandian Vaidyanathan,et al.  Analysis and Control of a 4-D Novel Hyperchaotic System , 2015, Chaos Modeling and Control Systems Design.

[23]  Sundarapandian Vaidyanathan,et al.  Analysis, Control and Synchronization of a Nine-Term 3-D Novel Chaotic System , 2015, Chaos Modeling and Control Systems Design.

[24]  Sundarapandian Vaidyanathan,et al.  Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation , 2015 .

[25]  GUANRONG CHEN,et al.  Can a Three-Dimensional Smooth Autonomous Quadratic Chaotic System Generate a Single Four-scroll Attractor? , 2004, Int. J. Bifurc. Chaos.

[26]  Sundarapandian Vaidyanathan,et al.  Backstepping Controller Design for the Global Chaos Synchronization of Sprott's Jerk Systems , 2015, Chaos Modeling and Control Systems Design.

[27]  Lin Wang,et al.  3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system , 2009 .

[28]  Sundarapandian Vaidyanathan,et al.  Chaos Modeling and Control Systems Design , 2014, Chaos Modeling and Control Systems Design.

[29]  Ahmad Taher Azar,et al.  Stabilization and Control of Mechanical Systems with Backlash , 2017 .

[30]  A. Harb,et al.  Chaos Control Using Fuzzy Controllers (Mamdani Model) , 2006 .

[31]  Sundarapandian Vaidyanathan,et al.  Analysis, synchronization and circuit design of a novel butterfly attractor , 2014 .

[32]  Ahmad Taher Azar,et al.  Robust IMC–PID tuning for cascade control systems with gain and phase margin specifications , 2014, Neural Computing and Applications.

[33]  Sundarapandian Vaidyanathan,et al.  Global chaos synchronisation of identical chaotic systems via novel sliding mode control method and its application to Zhu system , 2015, Int. J. Model. Identif. Control..