Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability...

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Dynamical Systems Theory

Background:

• Nonlinear dynamical systems present significant control challenges.
• Traditional controllers often struggle with complex, time-varying dynamics.
• Recurrent neural networks offer potential for adaptive control but require efficient structures.

Purpose of the Study:

• To propose and evaluate a diagonal recurrent neural network (DRNN) for adaptive control of nonlinear dynamical systems.
• To demonstrate the DRNN's capability in capturing and controlling complex dynamic behaviors.
• To compare the DRNN's performance against established neural network control methods.

Main Methods:

• Development of a modified recurrent neural network structure (DRNN) with self-recurrent neurons.
• Application of Lyapunov stability criterion to derive update rules for DRNN parameter adaptation.
• Comparative analysis of DRNN against multi-layer feedforward neural networks (MLFFNN) and fully connected recurrent neural networks (FCRNN).
• Testing robustness against parameter variations and external disturbances.

Main Results:

• DRNN effectively captures the dynamic behavior of nonlinear systems.
• Lyapunov-based update rules ensure system stability during adaptation.
• DRNN consistently outperforms MLFFNN in simulation examples.
• Robustness tests confirm the stability and effectiveness of DRNN under adverse conditions.

Conclusions:

• The proposed DRNN offers a superior adaptive control solution for nonlinear dynamical systems.
• DRNN's architecture is well-suited for modeling and controlling complex plant dynamics.
• The Lyapunov-based adaptation mechanism guarantees stable and effective control performance.