Finite-Time State Estimation for Coupled Markovian Neural Networks With Sensor Nonlinearities

Area of Science:

• Control Theory
• Artificial Neural Networks
• Stochastic Systems

Background:

• Coupled Markovian neural networks are crucial in various applications.
• Finite-time state estimation is essential for real-time control and analysis.
• Sensor nonlinearities and unknown Markov transition probabilities pose significant challenges.

Purpose of the Study:

• To develop a finite-time state estimator for coupled Markovian neural networks.
• To address challenges posed by sensor nonlinearities and partially unknown transition probabilities.
• To guarantee stochastic finite-time boundedness and stability of the estimation error.

Main Methods:

• A Luenberger-type state estimator is designed.
• The estimation error system is analyzed using the Kronecker product.
• Lyapunov stability theory is employed to establish sufficient conditions.
• Linear matrix inequalities are used to determine estimator gains.

Main Results:

• Sufficient conditions for stochastic finite-time boundedness and stability of the estimation error are derived.
• A novel Luenberger-type estimator is proposed for the considered network class.
• The effectiveness of the design method is validated through a numerical example.

Conclusions:

• The proposed method effectively achieves finite-time state estimation for complex neural network systems.
• The approach provides robust performance under sensor nonlinearities and uncertain Markovian dynamics.
• This work contributes to the advancement of state estimation techniques in nonlinear stochastic systems.