Detector-based boundary synchronization control of hidden Markov jump reaction-diffusion neural networks

Area of Science:

• Control Theory
• Neural Networks
• Stochastic Systems

Background:

• Reaction-diffusion neural networks exhibit complex dynamics and parameter variations.
• Hidden Markov models are used to represent abrupt changes in system parameters and structure.
• Traditional synchronization methods often require full state observability, which is not always feasible.

Purpose of the Study:

• To develop a passive synchronization control strategy for continuous-time hidden Markov jump reaction-diffusion neural networks.
• To address the challenge of unobservable states in Markov jump systems using a detector-based approach.
• To design a cost-effective boundary control method that reduces the number of required controllers.

Main Methods:

• A hidden Markov jump model is employed, incorporating both hidden and observed states.
• A detector is utilized to estimate the hidden states, relaxing the full observability assumption.
• A mode-dependent boundary synchronization controller is designed under Neumann boundary conditions.
• Convex optimization problems are solved to derive conditions for stability and passive performance.

Main Results:

• Sufficient conditions for guaranteeing system stability and expected passive performance are derived.
• The proposed boundary controller is shown to be more economical than full-domain controllers.
• Controller gains are obtained by solving convex optimization problems.
• The effectiveness and advantages of the proposed method are demonstrated through comparative examples.

Conclusions:

• The detector-based boundary control method effectively achieves passive synchronization for the studied neural networks.
• The approach offers a practical and cost-efficient solution compared to existing methods.
• The proposed framework provides a general way to handle varying levels of detection information.