Abstract
This paper addresses the master-slave synchronization problems of delayed neural networks with actuator failure based on stochastic sampled-data controller. To simplify the analysis process, only two different sampling periods whose occurrence probabilities follow the Bernoulli distribution are considered. In addition, it can be further extended to cases with multiple random sampling periods. The sampling system with random parameters is transformed into a continuous system through applying the input delay method. The novelty of this article is to consider the problem of actuator failure which may exist in the real world. By constructing a new type of Lyapunov-Krasovskii function (LKF), a sampling controller for neural networks synchronization system is designed. Using Jensens's inequality, Wirtinger's inequality and convex optimization methods, the stability criterion of neural networks with low conservativeness is acquired. Meanwhile, the controller gain matrix can be obtained through solving the linear matrix inequalities (LMIs). One numerical example provides feasibility and advantages of theoretical results.
Highlights
Nowadays, there has been a large number of researches on neural networks because they are widely used in various fields such as signal processing, image processing, pattern recognition, optimization, and associative memory design and so on [1], [2]
Based on the method of linear matrix inequalities (LMIs), many studies have devoted to the stability analysis of master-slave synchronization problems of neural networks
The sampled-data feedback controller u(t) used in synchronizing neural networks is generated by the zero-order holder (ZOH), which is mathematically modeled and includes using conventional digital-to-analog converter to complete practical signal reconstruction, and converting discrete signals into continuous signals
Summary
There has been a large number of researches on neural networks because they are widely used in various fields such as signal processing, image processing, pattern recognition, optimization, and associative memory design and so on [1], [2]. Based on the method of linear matrix inequalities (LMIs), many studies have devoted to the stability analysis of master-slave synchronization problems of neural networks. J. Tian et al.: Synchronization of Delayed Neural Networks With Actuator Failure the sampled-data only needs the information about the state of the system at the sampling instants [19]. Tian et al.: Synchronization of Delayed Neural Networks With Actuator Failure the sampled-data only needs the information about the state of the system at the sampling instants [19] The characteristic of this method is to reduce the transmission of information and improve the efficiency of control. The method can be applied to multiple random sampling times; (3) Unlike previous studies, the article proposes a reliable control scheme for the delayed neural network withactuator failure via stochastic sampled-data control. Sufficient conditions are presented to guarantee the stability and the desired controller can be obtained
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