Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

[1]  C. Zhai,et al.  Unique solutions for a new coupled system of fractional differential equations , 2018 .

[2]  Jing Li,et al.  Adaptive backstepping sliding mode control for wheel slip tracking of vehicle with uncertainty observer , 2018 .

[3]  Rickey Dubay,et al.  Adaptive fuzzy backstepping control for a class of uncertain nonlinear strict-feedback systems based on dynamic surface control approach , 2019, Expert Syst. Appl..

[4]  Juntao Fei,et al.  Fractional Sliding-Mode Control for Microgyroscope Based on Multilayer Recurrent Fuzzy Neural Network , 2022, IEEE Transactions on Fuzzy Systems.

[5]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[6]  Xingcheng Wang,et al.  Observer-Based Command Filtered Adaptive Neural Network Tracking Control for Fractional-Order Chaotic PMSM , 2019, IEEE Access.

[7]  Hamidreza Modares,et al.  Distributed Consensus Control for a Network of Incommensurate Fractional-Order Systems , 2019, IEEE Control Systems Letters.

[8]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[9]  F. Mainardi.  Fractional Calculus , 2018, Fractional Calculus.

[10]  Ali Azarbahram,et al.  Bipartite consensus control for fractional-order nonlinear multi-agent systems: An output constraint approach , 2020, Neurocomputing.

[11]  Xingcheng Wang,et al.  Command Filtering-Based Neural Network Control for Fractional-Order PMSM With Input Saturation , 2019, IEEE Access.

[12]  Clara-Mihaela Ionescu,et al.  The Human Respiratory System: An Analysis of the Interplay between Anatomy, Structure, Breathing and Fractal Dynamics , 2013 .

[13]  Haisheng Yu,et al.  Design and implementation of a novel adaptive backstepping control scheme for a PMSM with unknown load torque , 2019, IET Electric Power Applications.

[14]  Shaocheng Tong,et al.  Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[15]  Yanhong Luo,et al.  A new robust adaptive neural network backstepping control for single machine infinite power system with TCSC , 2020, IEEE/CAA Journal of Automatica Sinica.

[16]  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..

[17]  Shaocheng Tong,et al.  Neural-Network-Based Adaptive DSC Design for Switched Fractional-Order Nonlinear Systems , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Wenwu Yu,et al.  Fault-Tolerant Adaptive Fuzzy Tracking Control for Nonaffine Fractional-Order Full-State-Constrained MISO Systems With Actuator Failures , 2021, IEEE Transactions on Cybernetics.

[19]  Sundarapandian Vaidyanathan,et al.  Fractional-Order and Memristive Nonlinear Systems: Advances and Applications , 2017, Complex..

[20]  Jun Zhao,et al.  Switched-Observer-Based Adaptive Neural Control of MIMO Switched Nonlinear Systems With Unknown Control Gains , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Donglian Qi,et al.  Asymptotic pseudo-state stabilization of commensurate fractional-order nonlinear systems with additive disturbance , 2015 .

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

[23]  Zhiyao Ma,et al.  Adaptive Fuzzy Backstepping Dynamic Surface Control of Strict-Feedback Fractional-Order Uncertain Nonlinear Systems , 2020, IEEE Transactions on Fuzzy Systems.

[24]  Sandeep Kaur,et al.  Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control , 2018, Chaos, Solitons & Fractals.

[25]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[26]  Wei Wang,et al.  Adaptive Backstepping Control of Nonlinear Uncertain Systems With Quantized States , 2019, IEEE Transactions on Automatic Control.

[27]  Shaocheng Tong,et al.  Observed-Based Adaptive Fuzzy Tracking Control for Switched Nonlinear Systems With Dead-Zone , 2015, IEEE Transactions on Cybernetics.

[28]  Changhui Wang,et al.  Adaptive NN Tracking Control for Nonlinear Fractional Order Systems With Uncertainty and Input Saturation , 2018, IEEE Access.

[29]  Qingyou Liu,et al.  Adaptive fuzzy backstepping control for uncertain nonlinear systems with tracking error constraints , 2019, Advances in Mechanical Engineering.

[30]  H. Rahmani,et al.  On the Synchronization and Stabilization of fractional-order chaotic systems: Recent advances and future perspectives , 2020 .

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

[32]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Tracking Control for Strict-Feedback Nonlinear Systems With Unknown Control Gain Functions , 2020, IEEE Transactions on Cybernetics.

[33]  Xuhuan Wang.  Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients , 2018 .

[34]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[35]  Yangquan Chen,et al.  Two direct Tustin discretization methods for fractional-order differentiator/integrator , 2003, J. Frankl. Inst..

[36]  Jianping Cai,et al.  Adaptive Backstepping Control for a Class of Non-Triangular Structure Nonlinear Systems , 2020, IEEE Access.

[37]  Yuan Li,et al.  Adaptive Sliding Mode Control of a Class of Fractional-Order Nonlinear Systems With Input Uncertainties , 2019, IEEE Access.

[38]  Changhui Wang,et al.  An Adaptive Control of Fractional-Order Nonlinear Uncertain Systems with Input Saturation , 2019, Complex..

[39]  Lunhaojie Liu,et al.  Fuzzy Multiple Hidden Layer Recurrent Neural Control of Nonlinear System Using Terminal Sliding-Mode Controller , 2021, IEEE Transactions on Cybernetics.

[40]  Yogesh V. Hote,et al.  Experimental validation of fractional order internal model controller design on buck and boost converter , 2020 .

[41]  Juntao Fei,et al.  Fuzzy Double Hidden Layer Recurrent Neural Terminal Sliding Mode Control of Single-Phase Active Power Filter , 2021, IEEE transactions on fuzzy systems.