Adaptive Neural Network Synchronization Control for Uncertain Fractional-Order Time-Delay Chaotic Systems

Abstract

We propose an adaptive radial basis (RBF) neural network controller based on Lyapunov stability theory for uncertain fractional-order time-delay chaotic systems (FOTDCSs) with different time delays. The controller does not depend on the system model and can achieve synchronous control under the condition that nonlinear uncertainties and external disturbances are completely unknown. Stability analysis showed that the error system asymptotically tended to zero in combination with the relevant lemma. Numerical simulation results show the effectiveness of the controller.

The Multiple Frequency Conversion Sinusoidal Chaotic Neural Network and Its Application

“…Among the basic parameters, α represents the weight of the feedback signal received by the current neuron from other neurons, which is essentially used to balance the strength of chaotic dynamics and gradient descent [1][2][3][4]. z(0) and β mainly determine the initial value and decay rate of the self-feedback term (chaos term), respectively [1][2][3][4][5][6][7][8]. For the adjustment mechanism of α, z(0), and β, it is usually expected that the early stage is dominated by chaos search (improving the global search ability, avoiding local optimization), and the late stage is dominated by gradient convergence (improving the convergence speed).…”

“…Appropriate parameter selection of the model determines whether the algorithm can find the optimal solution quickly and accurately, which is always the difficulty faced by the TCNN class optimization model. Therefore, in order to facilitate rapid, effective and clear research and the use of appropriate parameter settings, this paper summarizes all parameter settings and selection guidance by referring to many literatures [1][2][3][4][5][6][7][8][9][10][17][18][19] and the above experimental analysis and verification, as shown in Table 2 To obtain good optimization performance of the model, it is necessary to properly select and balance the relationship between the basic parameters of the model and the MFCS parameter settings. The higher the complexity of the optimization problem, the stronger the non-monotony of MFCS is required.…”

“…Appropriate parameter selection of the model determines whether the algorithm can find the optimal solution quickly and accurately, which is always the difficulty faced by the TCNN class optimization model. Therefore, in order to facilitate rapid, effective and clear research and the use of appropriate parameter settings, this paper summarizes all parameter settings and selection guidance by referring to many literatures [1][2][3][4][5][6][7][8][9][10][17][18][19] and the above experimental analysis and verification, as shown in Table 2.…”

“…Annealing factor [0, 1] (0, 1) [0.001, 0.05] z(0) [6,7] Initial value of self feedback [0, 1] [0.7, 1] [0.6, 0.8] I 0 [7,8] Positive parameter (0, ∞) [0, 1] [0.45, 0.65] ε 0 [9,10] Steepness parameter [0, ∞) [0.01, 0.5] [0.01, 0.1] A n (0) [17] Initial value of the amplitude [0, ∞) (0, 1.2] [0.1, 0.8] ε n (0) [18] Initial value of teepness (0, ∞) [0.0044, 0.32] [0.01, 0.1] a n [18] Positive parameter (0, ∞) [19] Positive parameter (0, ∞) [0.56, 1.8] [0.6, 1.5] c n [19] Weighting coefficient (0, ∞)…”

“…The optimization mechanism of TCNN is the same as that of HNN, both of which adopt the gradient descent algorithm [6]. By introducing the chaotic dynamic (self-feedback) term, TCNN can make use of the ergodic property, pseudo-randomness and non-repeatability of chaos to avoid local optimization [7,8]. However, TCNN's chaotic global search performance is still limited due to the parameter setting, excitation function, annealing function and other factors, resulting in not being ideal [9,10].…”