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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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Saturation function-based continuous control on fixed-time synchronization of competitive neural networks.

Caicai Zheng1, Cheng Hu2, Juan Yu2

  • 1College of Mathematics and System Science, Xinjiang University, Urumqi, 830017, China.

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Summary
This summary is machine-generated.

This study introduces continuous control strategies for fixed-time (FXT) synchronization in competitive artificial neural networks (ANNs), simplifying analysis by integrating short-term and long-term memory models. The new approach avoids chattering and improves synchronization performance.

Keywords:
Competitive neural networkContinuous controlFXT synchronizationFixed-time (FXT) stabilitySaturation function

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Area of Science:

  • Artificial Intelligence
  • Computational Neuroscience
  • Control Theory

Background:

  • Fixed-time (FXT) synchronization of competitive artificial neural networks (ANNs) has been explored using discontinuous control and separate analysis of short-term memory (STM) and long-term memory (LTM).
  • Traditional methods suffer from complex derivations, stringent synchronization conditions, and performance degradation due to chattering from the signum function.

Purpose of the Study:

  • To address the challenges of complexity and performance reduction in FXT synchronization of competitive ANNs.
  • To develop novel continuous control schemes for achieving FXT synchronization with improved efficiency and stability.
  • To reduce the theoretical complexity by integrating STM and LTM models into a unified system.

Main Methods:

  • A high-dimensional system model is established by compressing the STM and LTM models of competitive ANNs.
  • A fixed-time stability theorem with switching differential conditions is developed, providing high-precision convergence time estimates.
  • Continuous pure power-law control schemes are designed using saturation functions, replacing the conventional signum function.

Main Results:

  • The proposed method simplifies theoretical analysis by unifying STM and LTM models.
  • Continuous control schemes based on saturation functions effectively achieve FXT synchronization, avoiding chattering.
  • Synchronization criteria are derived and validated through a numerical example, demonstrating applicability to image encryption.

Conclusions:

  • The study presents a more effective and less complex approach to achieving fixed-time synchronization in competitive ANNs.
  • The developed continuous control strategies offer improved performance and robustness compared to existing methods.
  • The findings have potential applications in areas such as secure image encryption.