Robust Control of Disturbed Fractional-Order Economical Chaotic Systems with Uncertain Parameters

This paper focuses on the robust control of fractional-order economical chaotic system (FOECS) with parametric uncertainties and external disturbances. The dynamical behavior of FOECS is studied by numerical simulation, and circuit implementations of FOECS are also given. Based on fractional-order Lyapunov stability theorems, a robust adaptive controller, which can guarantee that all signals remain bounded and the tracking error tends to a small region, is designed. The proposed method can be used to control a large range of fractional-order systems with system uncertainties. Fractional-order adaptation laws are constructed to update the estimation of adaptive parameters. Finally, the robustness and effectiveness of our control method are indicated by simulation results.

[1]  Heng Liu,et al.  Synchronization for fractional-order neural networks with full/under-actuation using fractional-order sliding mode control , 2017, International Journal of Machine Learning and Cybernetics.

[2]  Shantanu Das,et al.  Multi-objective Active Control Policy Design for Commensurate and Incommensurate Fractional Order Chaotic Financial Systems , 2015, ArXiv.

[3]  Norbert Heuer,et al.  Regularity of the solution to 1-D fractional order diffusion equations , 2016, Math. Comput..

[4]  Ahmad Hajipour,et al.  Analysis and circuit simulation of a novel nonlinear fractional incommensurate order financial system , 2016 .

[5]  Jinde Cao,et al.  Limit cycle oscillation in aeroelastic systems and its adaptive fractional-order fuzzy control , 2018, Int. J. Mach. Learn. Cybern..

[6]  Yaojin Lin,et al.  A graph approach for fuzzy-rough feature selection , 2020, Fuzzy Sets Syst..

[7]  I. Podlubny.  Fractional differential equations , 1998 .

[8]  Shenggang Li,et al.  Backstepping-Based Adaptive Fuzzy Synchronization Control for a Class of Fractional-Order Chaotic Systems with Input Saturation , 2019, Int. J. Fuzzy Syst..

[9]  Baogui Xin,et al.  Finite-time stabilizing a fractional-order chaotic financial system with market confidence , 2015 .

[10]  Wei Hu,et al.  Artificial bee colony algorithmbased parameter estimation of fractional-order chaotic system with time delay , 2017, IEEE/CAA Journal of Automatica Sinica.

[11]  Saptarshi Das,et al.  Chaos suppression in a fractional order financial system using intelligent regrouping PSO based fractional fuzzy control policy in the presence of fractional Gaussian noise , 2012 .

[12]  Yongping Pan,et al.  Adaptive Fuzzy Backstepping Control of Fractional-Order Nonlinear Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[13]  Ilknur Koca,et al.  Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order , 2016 .

[14]  Christos Volos,et al.  A simple three-dimensional fractional-order chaotic system without equilibrium: Dynamics, circuitry implementation, chaos control and synchronization , 2017 .

[15]  Zhen Wang,et al.  Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay , 2011, Comput. Math. Appl..

[16]  Abraham J. Arenas,et al.  Fractional Order Financial Models for Awareness and Trial Advertising Decisions , 2016 .

[17]  Manuel A. Duarte-Mermoud,et al.  Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[18]  Sara Dadras,et al.  Control of a fractional-order economical system via sliding mode , 2010 .

[19]  I. Petráš.  Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation , 2011 .

[20]  P. Balasubramaniam,et al.  Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system , 2015 .

[21]  Nooshin Bigdeli,et al.  Finite-time fractional-order adaptive intelligent backstepping sliding mode control of uncertain fractional-order chaotic systems , 2017, J. Frankl. Inst..

[22]  D. Baleanu,et al.  New aspects of the adaptive synchronization and hyperchaos suppression of a financial model , 2017 .

[23]  Yongguang Yu,et al.  Artificial Bee Colony Algorithm-based Parameter Estimation of Fractional-order Chaotic System with Time Delay , 2017 .

[24]  Jinde Cao,et al.  Lag projective synchronization of fractional-order delayed chaotic systems , 2019, J. Frankl. Inst..

[25]  Jinde Cao,et al.  Composite Learning Adaptive Dynamic Surface Control of Fractional-Order Nonlinear Systems , 2020, IEEE Transactions on Cybernetics.

[26]  Fuad E. Alsaadi,et al.  Adaptive fuzzy prescribed performance controller design for a class of uncertain fractional-order nonlinear systems with external disturbances , 2017, Neurocomputing.

[27]  P. Tse,et al.  Adaptive backstepping output feedback control for a class of nonlinear fractional order systems , 2016 .

[28]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[29]  高立克,et al.  Robust sliding mode control for fractional-order chaotic economical system with parameter uncertainty and external disturbance , 2015 .

[30]  Mohammad Saleh Tavazoei,et al.  Chaotic attractors in incommensurate fractional order systems , 2008 .

[31]  Karthikeyan Rajagopal,et al.  FPGA implementation of novel fractional-order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization , 2017 .

[32]  Kazuyuki Sasakura,et al.  On the dynamic behavior of Schinasi's business cycle model , 1994 .

[33]  Hongxing Wang,et al.  Robust Adaptive Control for Fractional-order Financial Chaotic Systems with System Uncertainties and External Disturbances , 2017, Inf. Technol. Control..

[34]  Wei-Ching Chen,et al.  Nonlinear dynamics and chaos in a fractional-order financial system , 2008 .

[35]  Jinde Cao,et al.  Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system , 2017 .

[36]  Mario Sportelli,et al.  A dynamic IS-LM model with delayed taxation revenues , 2005 .

[37]  Kolade M. Owolabi,et al.  Robust and adaptive techniques for numerical simulation of nonlinear partial differential equations of fractional order , 2017, Commun. Nonlinear Sci. Numer. Simul..

[38]  Hamid D. Taghirad,et al.  Adaptive robust control of fully-constrained cable driven parallel robots , 2015 .

[39]  Meng Joo Er,et al.  Adaptive Robust Online Constructive Fuzzy Control of a Complex Surface Vehicle System , 2016, IEEE Transactions on Cybernetics.

[40]  Abdesselem Boulkroune,et al.  Fuzzy generalized projective synchronization of incommensurate fractional-order chaotic systems , 2016, Neurocomputing.

[41]  Xiaoxiang Hu,et al.  Command filtered adaptive fuzzy backstepping control method of uncertain non-linear systems , 2016 .

[42]  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.

[43]  Igor Podlubny,et al.  Mittag-Leffler stability of fractional order nonlinear dynamic systems , 2009, Autom..

[44]  Jonas Gabrielsson,et al.  Does board independence influence financial performance in IPO firms? The moderating role of the national business system , 2017 .

[45]  Tiedong Ma,et al.  Robust sliding mode control for fractional-order chaotic economical system with parameter uncertainty and external disturbance* , 2015 .

[46]  Dumitru Baleanu,et al.  On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system , 2018 .