Projective synchronization for two nonidentical time-delayed fractional-order T–S fuzzy neural networks based on mixed 
                
                  
                
                $${H_\infty }$$
                
                  
                    
                      H
                      ∞
                    
                  
                
              /passive adaptive sliding mode control

The paper presents an improved adaptive sliding mode control method based on fuzzy neural networks for a class of nonlinear systems subjected to input nonlinearity with unknown model dynamics. The control scheme consists of the modified adaptive and the compensation controllers. The modified adaptive controller online approximates the unknown model dynamics and input nonlinearity and then constructs the sliding mode control law, while the compensation controller takes into account the approximation errors and keeps the system robust. Based on Lyapunov stability theorem, the proposed method can guarantee the asymptotic convergence to zero of the tracking error and provide the robust stability for the closed-loop system. In addition, due to the modification in controller design, the singularity problem that usually appears in indirect adaptive control techniques based on fuzzy/neural approximations is completely eliminated. Finally, the simulation results performed on an inverted pendulum system demonstrate the advanced functions and feasibility of the proposed adaptive control approach.

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Adaptive sliding mode control for a class of uncertain nonlinear fractional-order Hopfield neural networks

AIP Advances ◽

10.1063/1.5097374 ◽

2019 ◽

Vol 9 (6) ◽

pp. 065301 ◽

Cited By ~ 4

Author(s):

Bo Meng ◽

Zhicheng Wang ◽

Zhen Wang

Keyword(s):

Neural Networks ◽

Sliding Mode Control ◽

Fractional Order ◽

Sliding Mode ◽

Hopfield Neural Networks ◽

Adaptive Sliding Mode Control ◽

Adaptive Sliding Mode ◽

Mode Control

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Mixed H∞ and passive projective synchronization for fractional-order memristor-based neural networks with time delays via adaptive sliding mode control

Modern Physics Letters B ◽

10.1142/s0217984917501603 ◽

2017 ◽

Vol 31 (14) ◽

pp. 1750160 ◽

Cited By ~ 6

Author(s):

Shuai Song ◽

Xiaona Song ◽

Ines Tejado Balsera

Keyword(s):

Neural Networks ◽

Sliding Mode Control ◽

Fractional Order ◽

Time Delays ◽

Closed Loop ◽

Sliding Mode ◽

Projective Synchronization ◽

Adaptive Sliding Mode Control ◽

Closed Loop System ◽

Mode Control

This paper investigates the mixed [Formula: see text] and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks with time delays. Our aim is to design a controller such that, though the unavoidable phenomena of time delay and external disturbances is fully considered, the resulting closed-loop system is stable with a mixed [Formula: see text] and passive performance level. By combining sliding mode control and adaptive control methods, a novel adaptive sliding mode control strategy is designed for the synchronization of time-delayed FO dynamic networks. Via the application of FO system stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequalities. Based on the conditions, a desired controller which can guarantee the stability of the closed-loop system and also ensure a mixed [Formula: see text] and passive performance level is designed. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.

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