Fractional-order $$PI^{\lambda }D$$ sliding mode control for hypersonic vehicles with neural network disturbance compensator

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.

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Module-phase synchronization of fractional-order complex chaotic systems based on RBF neural network and sliding mode control

International Journal of Modern Physics B ◽

10.1142/s0217979220500502 ◽

2020 ◽

Vol 34 (07) ◽

pp. 2050050 ◽

Cited By ~ 1

Author(s):

Fuzhong Nian ◽

Xinmeng Liu ◽

Yaqiong Zhang ◽

Xuelong Yu

Keyword(s):

Neural Network ◽

Sliding Mode Control ◽

Fractional Order ◽

Chaotic Systems ◽

Phase Synchronization ◽

Sliding Mode ◽

Rbf Neural Network ◽

Order Complex ◽

Mode Control ◽

Complex Chaotic Systems

Combined with RBF neural network and sliding mode control, the synchronization between drive system and response system was achieved in module space and phase space, respectively (module-phase synchronization). The RBF neural network is used to estimate the unknown nonlinear function in the system. The module-phase synchronization of two fractional-order complex chaotic systems is implemented by the Lyapunov stability theory of fractional-order systems. Numerical simulations are provided to show the effectiveness of the analytical results.

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Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties

Fractal and Fractional ◽

10.3390/fractalfract4040050 ◽

2020 ◽

Vol 4 (4) ◽

pp. 50

Author(s):

Xuefeng Zhang ◽

Wenkai Huang

Keyword(s):

Neural Network ◽

Sliding Mode Control ◽

Fractional Order ◽

Sliding Mode ◽

Rbf Neural Network ◽

Linear Matrix ◽

Fractional Order Systems ◽

Sliding Surface ◽

Mode Control ◽

Necessary And Sufficient

This paper focuses on the sliding mode control (SMC) problem for a class of uncertain singular fractional order systems (SFOSs). The uncertainties occur in both state and derivative matrices. A radial basis function (RBF) neural network strategy was utilized to estimate the nonlinear terms of SFOSs. Firstly, by expanding the dimension of the SFOS, a novel sliding surface was constructed. A necessary and sufficient condition was given to ensure the admissibility of the SFOS while the system state moves on the sliding surface. The obtained results are linear matrix inequalities (LMIs), which are more general than the existing research. Then, the adaptive control law based on the RBF neural network was organized to guarantee that the SFOS reaches the sliding surface in a finite time. Finally, a simulation example is proposed to verify the validity of the designed procedures.

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