Adaptive neural PD control with semiglobal asymptotic stabilization guarantee.

Area of Science:

• Control Theory
• Nonlinear Systems
• Adaptive Control

Background:

• Uncertain affine nonlinear systems pose challenges for stabilization.
• Existing adaptive control methods often require knowledge of plant bounds or have complex designs.

Purpose of the Study:

• To develop a simplified adaptive control strategy for semiglobal asymptotic stabilization of uncertain nonlinear systems.
• To address the control singularity problem in adaptive control design.

Main Methods:

• Utilizing adaptive neural networks (specifically, linearly parameterized raised-cosine radial basis function networks) for optimal approximation.
• Implementing an integral Lyapunov function-based control law to prevent singularity.
• Introducing a variable-gain proportional-derivative (PD) control term that does not require plant bound knowledge.

Main Results:

• Demonstrated semiglobal asymptotic stabilization for a class of uncertain affine nonlinear systems, surpassing uniform ultimate boundedness.
• The proposed adaptive neural-PD control simplifies design and relaxes prior constraints on the system.
• Stability analysis is facilitated by the optimal approximation property of the neural network.

Conclusions:

• The developed adaptive neural-PD control offers a more straightforward and less restrictive approach to stabilizing uncertain nonlinear systems.
• Theoretical results are validated through two illustrative examples, confirming the effectiveness of the proposed method.