Abstract
This study is devoted to investigating the stabilization to exponential input-to-state stability (ISS) of a class of neural networks with time delay and external disturbances under the observer-based aperiodic intermittent control (APIC). Compared with the general neural networks, the state of the neural network investigated is not yet fully available. Correspondingly, an observer-based APIC is constructed, and moreover, neither the observer nor the controller requires the information of time delay. Then, the stabilization to exponential ISS of the neural network is realized severally by the observer-based time-triggered APIC (T-APIC) and the observer-based event-triggered APIC (E-APIC), and corresponding criteria are given. Furthermore, the minimum activation time rate (MATR) of the observer-based T-APIC and the observer-based E-APIC is estimated, respectively. Finally, a numerical example is given, which not only verifies the effectiveness of our results but also shows that the observer-based E-APIC is superior to the observer-based T-APIC and the observer-based periodic intermittent control (PIC) in control times and the minimum activation time rate, and the function of the observer-based T-APIC is also better than the observer-based PIC.
Highlights
Neural network, a mathematical model for information processing, can better simulate the working mechanism of the brain and plays a crucial role in artificial intelligence. e research on the dynamic behaviors of the neural network is the premise of the successful application of the neural network in many fields, such as associative memory, optimization problems, image recognition, different learning tasks, and so on [1,2,3,4,5,6,7]
By using a new multiple Lyapunov function and linear matrix inequalities, Lian and Zhang [14] discussed the exponential stability of a class of uncertain switched Cohen–Grossberg neural networks with interval time-varying, distributed delay, and average dwell time
According to the above elaboration, this study mainly focuses on exponential input-to-state stability of a class of neural networks with time delay and external disturbances under observer-based aperiodic intermittent control. e main work of this study is summarized as follows: (1) A state observer independent of time delay information is constructed, which is more practical because time delay information is often not and is not easy to obtain completely in some practical applications
Summary
A mathematical model for information processing, can better simulate the working mechanism of the brain and plays a crucial role in artificial intelligence. e research on the dynamic behaviors of the neural network is the premise of the successful application of the neural network in many fields, such as associative memory, optimization problems, image recognition, different learning tasks, and so on [1,2,3,4,5,6,7]. Erefore, it is more practical to study the stability of neural networks with time delay and external disturbances. Inspired by [30], it is very interesting to study the exponential ISS of the neural network by using the aperiodic intermittent control when the system state is not measurable. As far as we know, almost no scholars use aperiodic intermittent control to achieve the exponential ISS of neural networks with time delay and external disturbances when the system state is unmeasurable. According to the above elaboration, this study mainly focuses on exponential input-to-state stability of a class of neural networks with time delay and external disturbances under observer-based aperiodic intermittent control. The criterion to ensure the exponential input-to-state stability of the studied network is given, and the minimum activation time rate of the controller is evaluated. A numerical example is given to verify the effectiveness of the results. e conclusion and prospect are given in the sixth part
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