Adaptive critic-based quaternion neuro-fuzzy controller design with application to chaos control

Abstract Neuro-fuzzy control structures despite all of the advantages from both neural networks features and fuzzy inference engines always get in trouble due to a large number of fuzzy rules which is because of the high order of the system or the large number of divisions considered for each input. In this paper, a new adaptive neuro-fuzzy controller is proposed based on the quaternion numbers, and thus the mentioned problem of large rule numbers is solved by using the quaternion back propagation concept. Furthermore, utilizing reinforcement learning which assesses output value produced by a critic is another strength of the proposed method. Finally, in order to show the superiority and effectiveness of the proposed controller in comparison with conventional neuro-fuzzy ones, a complex and challenging chaos control problem which is a chaotic spinning disk control is provided.

[1]  Aria Alasty,et al.  Adaptive optimal multi-critic based neuro-fuzzy control of MIMO human musculoskeletal arm model , 2016, Neurocomputing.

[2]  M. Boroushaki,et al.  Adaptive Critic-based Neurofuzzy Controller for the Steam Generator Water Level , 2008, IEEE Transactions on Nuclear Science.

[3]  Richard S. Sutton,et al.  Temporal credit assignment in reinforcement learning , 1984 .

[4]  Jerry M. Mendel,et al.  Back-propagation fuzzy system as nonlinear dynamic system identifiers , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[5]  Jafar Abbaszadeh Chekan,et al.  Chaos control in lateral oscillations of spinning disk via linear optimal control of discrete systems , 2017 .

[6]  Kazuhiko Takahashi,et al.  Design of control systems using quaternion neural network and its application to inverse kinematics of robot manipulator , 2013, Proceedings of the 2013 IEEE/SICE International Symposium on System Integration.

[7]  Kwang Bo Cho,et al.  Radial basis function based adaptive fuzzy systems and their applications to system identification and prediction , 1996, Fuzzy Sets Syst..

[8]  Hamid R. Berenji,et al.  Learning and tuning fuzzy logic controllers through reinforcements , 1992, IEEE Trans. Neural Networks.

[9]  C. D. Mote,et al.  Non-linear oscillations of circular plates near a critical speed resonance , 1999 .

[10]  Kazuyuki Murase,et al.  Stabilization control of an inverted pendulum by complex-valued neuro-fuzzy learning algorithm , 2014, 2014 Joint 7th International Conference on Soft Computing and Intelligent Systems (SCIS) and 15th International Symposium on Advanced Intelligent Systems (ISIS).

[11]  Naoyoshi Yubazaki,et al.  A learning algorithm for tuning fuzzy rules based on the gradient descent method , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[12]  Akira Hirose,et al.  Complex-Valued Neural Networks: Theories and Applications , 2003 .

[13]  F. Lewis,et al.  Reinforcement Learning and Feedback Control: Using Natural Decision Methods to Design Optimal Adaptive Controllers , 2012, IEEE Control Systems.

[14]  H. Salarieh,et al.  Chaos control in lateral oscillations of spinning disks via nonlinear feedback , 2009 .

[15]  Amar Goléa,et al.  Observer-based adaptive control of robot manipulators: Fuzzy systems approach , 2008, Appl. Soft Comput..

[16]  M. A. Jalali,et al.  Phase space structure of spinning disks , 2006 .

[17]  Richard S. Sutton,et al.  Reinforcement Learning , 1992, Handbook of Machine Learning.

[18]  Naoyoshi Yubazaki,et al.  A Method of Fuzzy Rules Generation Based on Neuro-Fuzzy Learning Algorithm , 1996 .

[19]  Aria Alasty,et al.  Delayed feedback control of chaotic spinning disk via minimum entropy approach , 2008 .

[20]  Shengbo Eben Li,et al.  Advanced Machine Learning Approach for Lithium-Ion Battery State Estimation in Electric Vehicles , 2016, IEEE Transactions on Transportation Electrification.

[21]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[22]  Frank Klawonn,et al.  Combining Neural Networks and Fuzzy Controllers , 1993, FLAI.

[23]  T. Nitta,et al.  A quaternary version of the back-propagation algorithm , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[24]  Kazuyuki Murase,et al.  Quaternion neuro-fuzzy learning algorithm for generation of fuzzy rules , 2016, Neurocomputing.

[25]  Yongming Li,et al.  Adaptive output-feedback control design with prescribed performance for switched nonlinear systems , 2017, Autom..

[26]  Marzuki Khalid,et al.  Tuning of a neuro-fuzzy controller by genetic algorithm , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[27]  Nobuyuki Matsui,et al.  Quaternionic Multilayer Perceptron with Local Analyticity , 2012, Inf..

[28]  Elsayed A. Sallam,et al.  Adaptive fuzzy sliding mode control using supervisory fuzzy control for 3 DOF planar robot manipulators , 2011, Appl. Soft Comput..

[29]  Gang Feng,et al.  Robust adaptive output feedback control to a class of non-triangular stochastic nonlinear systems , 2018, Autom..

[30]  Mohammad Hassan Asemani,et al.  NON‐PDC Observer‐Based T‐S Fuzzy Tracking Controller Design and its Application in CHAOS Control , 2017 .

[31]  Csaba Szepesvári,et al.  Algorithms for Reinforcement Learning , 2010, Synthesis Lectures on Artificial Intelligence and Machine Learning.

[32]  Richard S. Sutton,et al.  Neuronlike adaptive elements that can solve difficult learning control problems , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[33]  Paul J. Werbos,et al.  Neurocontrol and fuzzy logic: Connections and designs , 1992, Int. J. Approx. Reason..

[34]  Kazuo Asakawa,et al.  Neural networks in Japan , 1994, CACM.

[35]  Yan Shi,et al.  A new approach of neuro-fuzzy learning algorithm for tuning fuzzy rules , 2000, Fuzzy Sets Syst..

[36]  Chuan-Kai Lin,et al.  Adaptive critic autopilot design of Bank-to-turn missiles using fuzzy basis function networks , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[37]  Aria Alasty,et al.  Adaptive critic-based neuro-fuzzy controller in multi-agents: Distributed behavioral control and path tracking , 2012, Neurocomputing.