Explain the principles of adaptive control and its architectures.

Adaptive control adjusts controller parameters in real-time to handle unknown or time-varying plant parameters. Two main architectures: Model Reference Adaptive Control (MRAC) - adjusts parameters to make plant behave like a reference model, uses Lyapunov/MIT rule for adaptation; Self-Tuning Regulator (STR) - estimates plant parameters online, designs controller based on estimates. Challenges include: persistent excitation requirement, handling unmodeled dynamics, transient performance, and stability proofs. Used when plant varies (wear, environmental changes) or initial uncertainty is large.