Stabilization of Rössler chaotic dynamical system using fuzzy logic control algorithm

This paper proposes a fuzzy logic control algorithm (FLCA) to stabilize the Rössler chaotic dynamical system. The fuzzy logic control system is based on a Takagi-Sugeno-Kang inference engine and the stability analysis in the sense of Lyapunov is carried out using Lyapunov’s direct method. The new FLCA is formulated to offer sufficient inequality stability conditions. The asymptotic complexity of our algorithm is analyzed and proved to be lower in comparison with that of linear matrix inequality-based FLCAs. A set of simulation results illustrates the effectiveness of the proposed FLCA.

[1]  Esteban Tlelo-Cuautle,et al.  Hyperchaotic Encryption for Secure E-Mail Communication , 2010, Emergent Web Intelligence.

[2]  Igor Skrjanc,et al.  Fault detection for nonlinear systems with uncertain parameters based on the interval fuzzy model , 2007, Eng. Appl. Artif. Intell..

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

[4]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

[5]  Dimitar Filev,et al.  Flexible models with evolving structure , 2004 .

[6]  Petr Dostál,et al.  Simulation of Adaptive LQ Control of Nonlinear Process , 2012 .

[7]  Z. Johanyák,et al.  A Hybrid Algorithm for Parameter Tuning in Fuzzy Model Identification , 2012, Acta Polytechnica Hungarica.

[8]  Chao-Jung Cheng,et al.  Robust synchronization of uncertain unified chaotic systems subject to noise and its application to secure communication , 2012, Appl. Math. Comput..

[9]  J. Vascak,et al.  Path planning in dynamic environment using Fuzzy Cognitive Maps , 2008, 2008 6th International Symposium on Applied Machine Intelligence and Informatics.

[10]  Yang Tang,et al.  Multiobjective synchronization of coupled systems. , 2011, Chaos.

[11]  Àngela Nebot,et al.  Fuzzy inductive reasoning: a consolidated approach to data-driven construction of complex dynamical systems , 2012, Int. J. Gen. Syst..

[12]  João Marcos Travassos Romano,et al.  Chaos-based communication systems in non-ideal channels , 2012 .

[13]  Lima,et al.  Suppression of chaos by resonant parametric perturbations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[14]  M. A. Aziz-Alaoui,et al.  Cluster synchronization analysis of complex dynamical networks by input-to-state stability , 2012 .

[15]  Igor Skrjanc,et al.  Identification of dynamical systems with a robust interval fuzzy model , 2005, Autom..

[16]  Sergio M. Savaresi,et al.  Optimal input design for direct data-driven tuning of model-reference controllers , 2013, Autom..

[17]  Witold Pedrycz,et al.  A framework of fuzzy hybrid systems for modelling and control , 2010, Int. J. Gen. Syst..

[18]  Xiaohong Zhang,et al.  Impulsive stability of chaotic systems represented by T-S model , 2009 .

[19]  Kazuo Tanaka,et al.  Stability analysis and design of fuzzy control systems , 1992 .

[20]  Z. Johanyák.  Student Evaluation Based On Fuzzy Rule Interpolation , 2010 .

[21]  Ricardo Sevilla-Escoboza,et al.  Two-channel opto-electronic chaotic communication system , 2012, J. Frankl. Inst..

[22]  József K. Tar,et al.  Generic two-degree-of-freedom linear and fuzzy controllers for integral processes , 2009, J. Frankl. Inst..

[23]  Yibei Nian,et al.  Controlling fractional order chaotic systems based on Takagi-Sugeno fuzzy model and adaptive adjustment mechanism , 2010 .

[24]  Lu Qi-Shao,et al.  Firing patterns and complete synchronization of coupled Hindmarsh-Rose neurons , 2005 .

[25]  Radu-Emil Precup,et al.  A survey on industrial applications of fuzzy control , 2011, Comput. Ind..

[26]  Wolfgang A. Halang,et al.  Non-linear feedback control of a novel chaotic system , 2009 .

[27]  Zhong Li.  Fuzzy Chaotic Systems: Modeling, Control, and Applications (Studies in Fuzziness and Soft Computing) , 2006 .

[28]  Claudia-Adina Dragos,et al.  Stability Analysis Results Concerning the Fuzzy Control of a Class of Nonlinear Time-Varying Systems , 2011 .

[29]  Oscar Castillo,et al.  A review on the applications of type-2 fuzzy logic in classification and pattern recognition , 2013, Expert Syst. Appl..

[30]  Jinde Cao,et al.  Exponential synchronization of stochastic perturbed chaotic delayed neural networks , 2007, Neurocomputing.

[31]  Yeung Yam,et al.  SVD-based complexity reduction to TS fuzzy models , 2002, IEEE Trans. Ind. Electron..

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

[33]  Petr Dostál,et al.  Adaptive LQ Approach Used in Conductivity Control inside Continuous-Stirred Tank Reactor , 2008 .

[34]  Lan Shu,et al.  Robust exponential stability of T-S fuzzy delayed systems with nonlinear perturbations , 2013, Int. J. Gen. Syst..

[35]  Krisztián Lamár,et al.  Average Probability of Failure of Aperiodically Operated Devices , 2013 .

[36]  Florin G. Filip.  A Decision-Making Perspective for Designing and Building Information Systems , 2012, Int. J. Comput. Commun. Control.

[37]  Dimitar Filev,et al.  Applied intelligent systems: blending fuzzy logic with conventional control , 2010, Int. J. Gen. Syst..

[38]  Zhidong Teng,et al.  General impulsive control of chaotic systems based on a TS fuzzy model , 2011, Fuzzy Sets Syst..

[39]  Endra Joelianto,et al.  ANFIS – Hybrid Reference Control for Improving Transient Response of Controlled Systems Using PID Controller , 2013 .

[40]  Farid Sheikholeslam,et al.  Stability analysis and design of fuzzy control systems , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[41]  Mihai Nadin,et al.  Concepts and fuzzy logic , 2012, Int. J. Gen. Syst..

[42]  Guanrong Chen,et al.  Fuzzy impulsive control of chaotic systems based on TS fuzzy model , 2009 .

[43]  Robert Babuska,et al.  Constrained distributed algebraic connectivity maximization in robotic networks , 2012, Autom..

[44]  P. Olver.  Nonlinear Systems , 2013 .

[45]  Plamen P. Angelov,et al.  A new type of simplified fuzzy rule-based system , 2012, Int. J. Gen. Syst..

[46]  George J. Klir,et al.  Concepts and fuzzy sets: Misunderstandings, misconceptions, and oversights , 2009, Int. J. Approx. Reason..

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

[48]  Horia-Nicolai L. Teodorescu,et al.  Characterization of nonlinear dynamic systems for engineering purposes – a partial review , 2012, Int. J. Gen. Syst..

[49]  Shahriar Gharibzadeh,et al.  Some remarks on chaotic systems , 2012, Int. J. Gen. Syst..

[50]  Cheng-Wu Chen,et al.  RETRACTED: Applications of the fuzzy Lyapunov linear matrix inequality criterion to a chaotic structural system , 2012 .

[51]  Reza Shahnazi,et al.  Synchronization of general chaotic systems using neural controllers with application to secure communication , 2011, Neural Computing and Applications.

[52]  O. Rössler.  An equation for continuous chaos , 1976 .

[53]  Plamen P. Angelov,et al.  Flexible models with evolving structure , 2004, Int. J. Intell. Syst..

[54]  Stefan Preitl,et al.  Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems , 2013, Expert Syst. Appl..

[55]  Horia-Nicolai Teodorescu.  Taylor and Bi-local Piecewise Approximations with Neuro-Fuzzy Systems , 2012 .

[56]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

[57]  Radu-Emil Precup,et al.  Stability analysis of a class of MIMO fuzzy control systems , 2010, International Conference on Fuzzy Systems.

[58]  Gunawan Dewantoro,et al.  Fuzzy Sliding Mode Control for Enhancing Injection Velocity Performance in Injection Molding Machine , 2013 .

[59]  Pedro Isasi,et al.  Predicting IPO Underpricing with Genetic Algorithms , 2012 .

[60]  Marius-Lucian Tomescu,et al.  Fuzzy Logic Control System Stability Analysis Based on Lyapunov's Direct Method , 2009, Int. J. Comput. Commun. Control.