Hybrid projective synchronization of fractional-order memristor-based neural networks with time delays

Time delays are frequently appearing in many real-life phenomena and the presence of time delays in chaotic systems enriches its complexities. The analysis of fractional-order chaotic real nonlinear systems with time delays has a plenty of interesting results but the research on fractional-order chaotic complex nonlinear systems with time delays is in the primary stage. This paper studies the problem of hybrid projective synchronization (HPS) of fractional-order chaotic complex nonlinear systems with time delays. HPS is one of the extensions of projective synchronization, in which different state vectors can be synchronized up to different scaling factors. Based on Laplace transformation and the stability theory of linear fractional-order systems, a suitable nonlinear controller is designed to achieve synchronization between the master and slave fractional-order chaotic complex nonlinear systems with time delays in the sense of HPS with different scaling factors. Finally, the HPS between fractional-order delayed complex Lorenz system and fractional-order delayed complex Chen system and that of fractional-order delayed complex Lorenz system and fractional-order delayed complex Lu system are taken into account to demonstrate the effectiveness and feasibility of the proposed HPS techniques in the numerical example section.

Download Full-text

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.

Download Full-text