Model Reference Adaptive Control Program Based on Lyapunov Stability Theory

The Model Reference Adaptive Control (MRAC) program based on Lyapunov stability theory is a control system designed to maintain stability even under unknown or uncertain conditions. This program employs MRAC technology, which enhances control system performance by tracking a reference model. In the MRAC framework, the controller output is continuously adjusted to minimize the error between the reference model's output and the actual system output. The controller monitors system behavior and adapts its parameters based on real-time feedback to maximize stability. Key implementation aspects include:

- Lyapunov function formulation to guarantee global stability

- Adaptive law derivation using gradient or MIT rule approaches

- Real-time parameter update loops with bounded gain conditions

This stability theory finds extensive applications in autonomous control domains such as robotics, aircraft, and automotive systems, where the code typically involves error dynamics calculation, adaptive gain scheduling, and stability margin verification through Lyapunov derivative analysis.