Neural Observer With Lyapunov Stability Guarantee for Uncertain Nonlinear Systems.

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Nonlinear Dynamics

Background:

• Traditional observers struggle with uncertain nonlinear systems.
• Accurate state estimation is crucial for control and monitoring.
• Neural networks offer powerful function approximation capabilities.

Purpose of the Study:

• To propose a novel nonlinear observer based on neural networks (NNs) called neural observers.
• To address observation tasks for both linear time-invariant (LTI) and uncertain nonlinear systems.
• To develop a method capable of real-time uncertainty measurement.

Main Methods:

• Designing neural observers inspired by active disturbance rejection control for uncertain systems.
• Employing linear matrix inequalities (LMIs) for stability analysis and guaranteeing exponential convergence rates.
• Analyzing observability and controllability of system matrices for LMI solution existence.

Main Results:

• Demonstrated stability and guaranteed exponential convergence for LTI and uncertain nonlinear systems using neural observers.
• Showcased that observation problems can be solved using only LMIs.
• Verified the effectiveness of neural observers through simulations on diverse models (X-29A aircraft, nonlinear pendulum, four-wheel steering vehicle).

Conclusions:

• Neural observers provide a robust and effective solution for state estimation in complex systems.
• The proposed method offers guaranteed stability and real-time uncertainty handling.
• LMIs, coupled with system properties like observability and controllability, are key to the observer's success.