Fast disturbance-observer-based robust integral terminal sliding mode control of a hyperchaotic memristor oscillator

Abstract This paper is concerned with the stabilization and tracking control of a hyperchaotic memristor oscillator using a novel disturbance-observer-based integral terminal sliding mode control. Firstly, the dynamic behaviours of the hyperchaotic memristor oscillator are investigated. Afterward, the fast disturbance-observer is combined with integral terminal sliding mode control for multi-input-multi-output (MIMO) nonlinear relative degree one systems in presences of external disturbance, unknown input saturation, and control singularity. The Lyapunov stability theorem is implemented to prove the finite time convergence of the closed-loop system. Furthermore, to specify the parameters of the proposed controller, the genetic algorithm optimization is applied to decrease chattering of the system’s response. Simulation results are presented to show the appropriate performance of the proposed control scheme in terms of stabilization and tracking control in the presence of external disturbances and input saturation.

[1]  Moosa Ayati,et al.  Integral sliding mode control for nonlinear damped model of arch microbeams , 2019 .

[2]  Fairouz Tchier,et al.  Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer , 2017 .

[3]  Viet-Thanh Pham,et al.  Bifurcation analysis and circuit realization for multiple-delayed Wang–Chen system with hidden chaotic attractors , 2016 .

[4]  Saleh Mobayen,et al.  Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control. , 2018, ISA transactions.

[5]  Antonella Ferrara,et al.  Robust Model Predictive Control With Integral Sliding Mode in Continuous-Time Sampled-Data Nonlinear Systems , 2011, IEEE Transactions on Automatic Control.

[6]  Moosa Ayati,et al.  Disturbance-observer-based fuzzy terminal sliding mode control for MIMO uncertain nonlinear systems , 2019, Applied Mathematical Modelling.

[7]  Marcelo A. Savi,et al.  Adaptive fuzzy sliding mode control of smart structures , 2013 .

[8]  Viet-Thanh Pham,et al.  Entropy Analysis and Neural Network-Based Adaptive Control of a Non-Equilibrium Four-Dimensional Chaotic System with Hidden Attractors , 2019, Entropy.

[9]  Zhouchao Wei,et al.  Delayed feedback control and bifurcation analysis of the generalized Sprott B system with hidden attractors , 2015 .

[10]  Lee Sun-Jin.  From Chaos to Order , 2011 .

[11]  Sarah K. Spurgeon,et al.  Robust sliding mode control of uncertain nonlinear systems , 1997 .

[12]  D. Ho,et al.  Design of sliding mode control for nonlinear stochastic systems subject to actuator nonlinearity , 2006 .

[13]  Viet-Thanh Pham,et al.  Synchronization and circuit design of a chaotic system with coexisting hidden attractors , 2015 .

[14]  Chian-Song Chiu,et al.  Derivative and integral terminal sliding mode control for a class of MIMO nonlinear systems , 2012, Autom..

[15]  Zhouchao Wei,et al.  Hidden Hyperchaotic Attractors in a Modified Lorenz-Stenflo System with Only One Stable Equilibrium , 2014, Int. J. Bifurc. Chaos.

[16]  Ke Zhang,et al.  Iterative Learning Fault Estimation Design for Nonlinear System with Random Trial Length , 2017, Complex..

[17]  Rongrong Wang,et al.  A new finding of the existence of hidden hyperchaotic attractors with no equilibria , 2014, Math. Comput. Simul..

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

[19]  Zhouchao Wei,et al.  Dynamics and delayed feedback control for a 3D jerk system with hidden attractor , 2015 .

[20]  Dylan Dah-Chuan Lu,et al.  Single-Stage AC/DC Boost–Forward Converter With High Power Factor and Regulated Bus and Output Voltages , 2009, IEEE Transactions on Industrial Electronics.

[21]  David L. Levy.  CHAOS THEORY AND STRATEGY: THEORY, APPLICATION, AND MANAGERIAL IMPLICATIONS , 2007 .

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

[23]  Akif Akgul,et al.  Hopf Bifurcation, Positively Invariant Set, and Physical Realization of a New Four-Dimensional Hyperchaotic Financial System , 2017 .

[24]  Akif Akgul,et al.  Complete analysis and engineering applications of a megastable nonlinear oscillator , 2018, International Journal of Non-Linear Mechanics.

[25]  Wen-Hua Chen,et al.  Sliding mode control for a class of uncertain nonlinear system based on disturbance observer , 2009 .

[26]  Hong Ren Wu,et al.  A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators , 1994, IEEE Trans. Autom. Control..

[27]  Viet-Thanh Pham,et al.  A hyperchaotic memristor oscillator with fuzzy based chaos control and LQR based chaos synchronization , 2018, AEU - International Journal of Electronics and Communications.

[28]  Amirreza Kosari,et al.  An optimal fuzzy PID control approach for docking maneuver of two spacecraft: Orientational motion , 2017 .

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

[30]  Weisheng Yan,et al.  Terminal sliding mode-based cooperative tracking control for non-linear dynamic systems , 2017 .

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

[32]  Mohammad Hassan Khooban,et al.  Sliding mode disturbance observer control based on adaptive synchronization in a class of fractional‐order chaotic systems , 2018, International Journal of Adaptive Control and Signal Processing.

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

[34]  Mou Chen,et al.  Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems. , 2013, ISA transactions.

[35]  M. Di Ventra,et al.  Chaotic memristor , 2011, 1101.4618.

[36]  Franck Plestan,et al.  Higher order sliding mode control based on integral sliding mode , 2007, Autom..

[37]  Hadi Jahanshahi,et al.  Smooth control of HIV/AIDS infection using a robust adaptive scheme with decoupled sliding mode supervision , 2018, The European Physical Journal Special Topics.

[38]  Saleh Mobayen,et al.  Design of novel adaptive sliding mode controller for perturbed Chameleon hidden chaotic flow , 2018 .

[39]  Shaocheng Tong,et al.  Fuzzy adaptive sliding-mode control for MIMO nonlinear systems , 2003, IEEE Trans. Fuzzy Syst..

[40]  Xiaodi Li,et al.  Synchronization of Identical and Nonidentical Memristor-based Chaotic Systems Via Active Backstepping Control Technique , 2015, Circuits Syst. Signal Process..

[41]  Jinde Cao,et al.  Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances , 2017, Appl. Math. Comput..

[42]  Syed Shakib Sarwar,et al.  Memristor-Based Nonvolatile Random Access Memory: Hybrid Architecture for Low Power Compact Memory Design , 2013, IEEE Access.

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

[44]  Yu-Sheng Lu,et al.  Sliding-Mode Disturbance Observer With Switching-Gain Adaptation and Its Application to Optical Disk Drives , 2009, IEEE Transactions on Industrial Electronics.

[45]  M. Yao,et al.  Study of hidden attractors, multiple limit cycles from Hopf bifurcation and boundedness of motion in the generalized hyperchaotic Rabinovich system , 2015 .

[46]  Zhouchao Wei,et al.  Delayed feedback on the 3-D chaotic system only with two stable node-foci , 2012, Comput. Math. Appl..

[47]  Mohamed Jemli,et al.  Nonlinear integral sliding mode control design of photovoltaic pumping system: Real time implementation. , 2017, ISA transactions.

[48]  Mahdi Fakoor,et al.  Adaptive Fuzzy PID Control Strategy for Spacecraft Attitude Control , 2019, Int. J. Fuzzy Syst..

[49]  Viet-Thanh Pham,et al.  Robot Motion Planning in an Unknown Environment with Danger Space , 2019, Electronics.

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

[51]  Viet-Thanh Pham,et al.  Optimal adaptive higher order controllers subject to sliding modes for a carrier system , 2018 .

[52]  Xinghuo Yu,et al.  Terminal sliding mode control of MIMO linear systems , 1997 .

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

[54]  Euntai Kim,et al.  A fuzzy disturbance observer and its application to control , 2002, IEEE Trans. Fuzzy Syst..

[55]  Shukai Duan,et al.  Memristor-Based Cellular Nonlinear/Neural Network: Design, Analysis, and Applications , 2015, IEEE Transactions on Neural Networks and Learning Systems.