Adaptive Synchronization for a Class of Uncertain Fractional-Order Neural Networks

Abstract

In this paper, synchronization for a class of uncertain fractional-order neural networks subject to external disturbances and disturbed system parameters is studied. Based on the fractional-order extension of the Lyapunov stability criterion, an adaptive synchronization controller is designed, and fractional-order adaptation law is proposed to update the controller parameter online. The proposed controller can guarantee that the synchronization errors between two uncertain fractional-order neural networks converge to zero asymptotically. By using some proposed lemmas, the quadratic Lyapunov functions are employed in the stability analysis. Finally, numerical simulations are presented to confirm the effectiveness of the proposed method.

Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

“…It was hard to use physically. In the following parts, the Caputo's derivative will be used [24]. Firstly, we give some definitions and lemmas.…”

“…The control problems of all kinds of FOS were studied recently [17][18][19][20][21]. Many researchers focused on fractional-order neural networks (FONNs) [22][23][24][25][26][27]. Cao et al [28] investigated the existence and uniqueness of the nontrivial solution of NNs and the uniform stability of the FONNs.…”

“…Mathematical Problems in Engineering [24] have researched adaptive synchronization of a class of FONNs. It is well known that time delay is unavoidable due to finite switching speeds of the amplifiers, and it may cause oscillations or instability of dynamic systems.…”

Prescribed performance synchronization controller design of fractional-order chaotic systems: An adaptive neural network control approach

“…4,[26][27][28][29][30][31][32][33][34][35][36][37][38][39] It should be emphasized that the research results on synchronizing FOCSs based on neural networks control methods are very few. In our work, we will design a PP synchronization controller for uncertain FOCSs.…”

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

“…[16][17][18][19][20][21][22][23][24][25] In most of above literatures, the quadratic Lyapunov functions (for example, V (t) = T (t)x(t)) are used in the stability analysis. However, we know that the fractional-order derivative of these functions has very complicated forms, 1-3 so it is very hard to analyze the stability of the closed-loop system.…”