A hyperchaotic memristor oscillator with fuzzy based chaos control and LQR based chaos synchronization

Abstract Chaotic and hyperchaotic systems with interesting behaviors have been of interest in the recent years. In this paper we introduce a hyperchaotic memristor oscillator which shows both stable and unstable fixed points. Such systems have been less investigated in the literatures. It should also to be noted that the proposed hyperchaotic system has only one nonlinearity which is a flux controlled memristor. Depending on the control parameter, the system displays different behaviors and coexisting attractors. A linear quadratic regulator based synchronization of the proposed hyperchaotic system is designed and numerically analyzed. We also design such a fuzzy based PID controller for chaos control in such a memristor oscillator.

[1]  Sundarapandian Vaidyanathan,et al.  Hyperchaos, qualitative analysis, control and synchronisation of a ten-term 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities , 2015, Int. J. Model. Identif. Control..

[2]  Ju H. Park,et al.  Robust adaptive backstepping synchronization for a class of uncertain chaotic systems using fuzzy disturbance observer , 2012 .

[3]  Dongsheng Yu,et al.  Hyperchaos in a memristor-Based Modified Canonical Chua's Circuit , 2012, Int. J. Bifurc. Chaos.

[4]  Tamara Nestorović,et al.  Robust observer-based adaptive fuzzy sliding mode controller , 2016 .

[5]  Ligang Wu,et al.  Optimal Guaranteed Cost Sliding-Mode Control of Interval Type-2 Fuzzy Time-Delay Systems , 2018, IEEE Transactions on Fuzzy Systems.

[6]  Amirreza Kosari,et al.  Optimal FPID Control Approach for a Docking Maneuver of Two Spacecraft: Translational Motion , 2017 .

[7]  Radu-Emil Precup,et al.  Stable Fuzzy Logic Control of Generalized van der Pol Oscillator , 2011 .

[8]  Guanrong Chen,et al.  Generating Hyperchaos via State Feedback Control , 2005, Int. J. Bifurc. Chaos.

[9]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[10]  Xingyuan Wang,et al.  A hyperchaos generated from Lorenz system , 2008 .

[11]  Peng Shi,et al.  Dissipativity-Based Reliable Control for Fuzzy Markov Jump Systems With Actuator Faults , 2017, IEEE Transactions on Cybernetics.

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

[13]  Jianbin Qiu,et al.  A Piecewise-Markovian Lyapunov Approach to Reliable Output Feedback Control for Fuzzy-Affine Systems With Time-Delays and Actuator Faults , 2018, IEEE Transactions on Cybernetics.

[14]  Sundarapandian Vaidyanathan,et al.  A no-equilibrium hyperchaotic system with a cubic nonlinear term , 2016 .

[15]  Mohammad Shahrokhi,et al.  Observer-based adaptive fuzzy controller for nonlinear systems with unknown control directions and input saturation , 2017, Fuzzy Sets Syst..

[16]  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..

[17]  Ligang Wu,et al.  Fault Detection Filtering for Nonhomogeneous Markovian Jump Systems via a Fuzzy Approach , 2018, IEEE Transactions on Fuzzy Systems.

[18]  Svetoslav Nikolov,et al.  Occurrence of regular, chaotic and hyperchaotic behavior in a family of modified Rossler hyperchaotic systems , 2004 .

[19]  Hadi Jahanshahi,et al.  Multi-objective optimized fuzzy-PID controllers for fourth order nonlinear systems , 2016 .

[20]  Ligang Wu,et al.  Reliable Filter Design for Sensor Networks Using Type-2 Fuzzy Framework , 2017, IEEE Transactions on Industrial Informatics.

[21]  Moosa Ayati,et al.  Adaptive Fuzzy Control of Nonlinear in Parameters Uncertain Chaotic Systems Using Improved Speed Gradient Method , 2012, Circuits Syst. Signal Process..

[22]  Guangyi Wang,et al.  Coexisting Oscillation and Extreme Multistability for a Memcapacitor-Based Circuit , 2017 .

[23]  K. Åström,et al.  Revisiting The Ziegler‐Nichols Tuning Rules For Pi Control , 2002 .

[24]  Xiaofeng Liao,et al.  Synchronization and chaos in coupled memristor-based FitzHugh-Nagumo circuits with memristor synapse , 2017 .

[25]  Soheil Ganjefar,et al.  Intelligent power system stabilizer design using adaptive fuzzy sliding mode controller , 2017, Neurocomputing.

[26]  Ruy Barboza.  Dynamics of a hyperchaotic Lorenz System , 2007, Int. J. Bifurc. Chaos.

[27]  Amir Poursamad,et al.  Robust adaptive fuzzy control of unknown chaotic systems , 2009, Appl. Soft Comput..

[28]  Zhulin Wang,et al.  A new hyperchaotic circuit with two memristors and its application in image encryption , 2016 .

[29]  O. Rössler.  An equation for hyperchaos , 1979 .

[30]  G C Kember,et al.  Online optimization of fuzzy-PID control of a thermal process. , 2005, ISA transactions.

[31]  William L. Luyben,et al.  Essentials of Process Control , 1996 .

[32]  Karthikeyan Rajagopal,et al.  Bifurcation and chaos in time delayed fractional order chaotic memfractor oscillator and its sliding mode synchronization with uncertainties , 2017 .

[33]  Qingling Zhang,et al.  Delay-estimation-based adaptive fuzzy memory control for a class of uncertain nonlinear time-delay systems , 2017, Fuzzy Sets Syst..

[34]  Simin Yu,et al.  Generating hyperchaotic Lü attractor via state feedback control , 2006 .

[35]  Qingdu Li,et al.  Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria , 2015 .