Differential Neural Network Identifier for Dynamical Systems With Time-Varying State Constraints.

Area of Science:

• Robotics and Control Systems
• Artificial Intelligence
• Nonlinear System Identification

Background:

• Traditional nonparametric identifiers often struggle with systems subject to state constraints.
• Ensuring system states remain within predefined bounds is crucial for safety and performance in many applications.
• Differential neural networks (DNNs) offer a promising framework for continuous dynamic system identification.

Purpose of the Study:

• To develop a state nonparametric identifier based on differential neural networks (DNNs) that incorporates time-dependent state constraints.
• To design parameter adjustment laws using control barrier Lyapunov functions (BLFs) to enforce these constraints.
• To evaluate the performance of the proposed identifier against a standard identifier that ignores state restrictions.

Main Methods:

• Utilizing differential neural networks (DNNs) for continuous dynamic system modeling.
• Developing parameter update laws based on control barrier Lyapunov functions (BLFs).
• Solving nonlinear differential equations and Riccati equations for learning laws considering state constraints.

Main Results:

• The proposed identifier, incorporating state constraints via BLFs, demonstrated improved identification accuracy.
• Numerical evaluation on a robotic arm system showed a 4.2 times reduction in mean square error compared to a constraint-ignoring identifier.
• The identifier successfully ensured that system states did not transgress the predefined time-dependent limits.

Conclusions:

• The integration of BLFs with DNNs provides an effective method for nonparametric system identification under state constraints.
• The developed learning laws ensure robust identification while respecting system limitations.
• This approach offers significant advantages for applications requiring precise control and safety, such as flight simulators and robotics.