Abstract
In this paper, we are concerned with the synchronization scheme for fractional-order bidirectional associative memory (BAM) neural networks, where both synaptic transmission delay and impulsive effect are considered. By constructing Lyapunov functional, sufficient conditions are established to ensure the Mittag–Leffler synchronization. Based on Pontryagin’s maximum principle with delay, time-dependent control gains are obtained, which minimize the accumulative errors within the limitation of actuator saturation during the Mittag–Leffler synchronization. Numerical simulations are carried out to illustrate the feasibility and effectiveness of theoretical results with the help of the modified predictor-corrector algorithm and the forward-backward sweep method.
Highlights
Forward and backward information flow is introduced in neural networks to produce two-way associative search for stored stimulus-response associations
During the Mittag–Leffler synchronization, it is of great practical significance to realize optimal synchronization control which minimizes the accumulative errors within the limitation of actuator saturation
Based on the modified predictor-corrector algorithm [4, 8] and the forward-backward sweep method [14], we derive the time-dependent control gains, which minimizes the accumulative errors within the limitation of actuator saturation
Summary
Forward and backward information flow is introduced in neural networks to produce two-way associative search for stored stimulus-response associations. There have been several works on synchronization problems with respect to the fractional-order neural networks via various control approaches such as impulsive control [35], linear feedback control [26], sliding model control [6], eventtriggered control [22] and so on. Ding et al [9] studied the synchronization for a class of fractional-order BAM neural networks with time delays and discontinuous activation functions, where the state feedback http://www.journals.vu.lt/nonlinear-analysis. Mittag–Leffler synchronization for impulsive fractional-order BAM neural networks and impulsive controllers are designed to ensure the Mittag–Leffler synchronization, respectively. It is necessary to take the impulsive effects into account [13, 19] To this end, we consider the following impulsive fractional-order BAM neural network with synaptic transmission delay: m.
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