Finite-time H_∞ output synchronization for DCRDNNs with multiple delayed and adaptive output couplings

Area of Science:

• Control Systems Engineering
• Computational Neuroscience
• Applied Mathematics

Background:

• Reaction-diffusion neural networks (DCRDNNs) are crucial for modeling complex spatio-temporal dynamics.
• Synchronization of DCRDNNs is essential for distributed information processing and secure communication.
• Existing methods often struggle with finite-time convergence and external disturbances.

Purpose of the Study:

• To investigate and solve the finite-time H∞ output synchronization (FTHOS) problem for DCRDNNs.
• To develop adaptive control strategies for systems with multiple delayed and adaptive output couplings.
• To analyze synchronization performance under external disturbances.

Main Methods:

• Design of an adaptive law to adjust output coupling weights based on output information.
• Development of a controller to achieve FTHOS.
• Formulation of a corollary for finite-time output synchronization (FTOS) in the absence of disturbances.
• Proposal of a novel adaptive scheme for H∞ output synchronization (HOS) with delayed couplings.

Main Results:

• The proposed adaptive law and controller successfully ensure FTHOS for DCRDNNs.
• A specific case without external disturbances yields a corollary on FTOS.
• A new adaptive scheme guarantees HOS in DCRDNNs with delayed couplings.
• Simulation results validate the effectiveness of the developed synchronization criteria.

Conclusions:

• The study provides effective solutions for finite-time synchronization problems in DCRDNNs.
• Adaptive control strategies are robust to external disturbances and network delays.
• The findings contribute to the theoretical understanding and practical application of synchronized neural networks.