Saturation function-based continuous control on fixed-time synchronization of competitive neural networks

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.