Discrete-time reduced order neural observers for uncertain nonlinear systems.

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Nonlinear Dynamics

Background:

• Accurate state estimation is crucial for controlling nonlinear systems, especially when system models are unknown.
• Traditional observers struggle with uncertainties and unknown dynamics, limiting their applicability.
• Neural networks offer a powerful tool for approximating unknown system dynamics.

Purpose of the Study:

• To develop a novel discrete-time reduced-order neural observer for nonlinear systems with unknown models.
• To ensure the observer's robustness against internal and external uncertainties.
• To provide a rigorous stability analysis for the proposed estimation scheme.

Main Methods:

• Utilized a discrete-time recurrent high order neural network (RHONN) for system modeling.
• Employed an extended Kalman filter (EKF)-based algorithm for RHONN training in a parallel configuration.
• Applied Lyapunov stability theory to prove the convergence of the estimation error.

Main Results:

• Demonstrated the robustness of the proposed neural observer in the presence of system uncertainties.
• Validated the observer's performance through simulation studies on a representative nonlinear oscillator.
• Confirmed the theoretical stability of the estimation error bounds.

Conclusions:

• The proposed discrete-time reduced-order neural observer effectively estimates states for unknown nonlinear systems.
• The EKF-trained RHONN provides a robust and stable solution for state estimation under uncertainties.
• The method is applicable to real-world nonlinear systems, as shown by the nonlinear oscillator example.