Uncertainty as State

Why Δ Must Be a State

Treating uncertainty Δ as a single fixed bound hides critical information: where and how degradation manifests.

True Robust Control treats Δ as a state variable.

Decomposition of Δ

Δ is monitored in three domains:

Low-Frequency Component

• Tracking degradation
• Gain reduction
• Increased friction

Risk:

• Loss of performance
• Steady-state error

High-Frequency Component

• Unmodeled dynamics
• Delay increase
• Resonance amplification

Risk:

• Loss of stability margin
• Oscillation

Input-Side Component

• Increased control effort
• Saturation
• Mechanical stress

Risk:

• Hardware damage
• Actuator failure

Operational Threshold: 0.8

• ∥Δ∥∞ = 1.0 → theoretical guarantee failure
• Waiting until 1.0 is reactive and unsafe

0.8 is chosen as a proactive operational threshold:

• Still within guaranteed region
• Close enough to anticipate worst-case behavior

FSM Interpretation

When any component reaches 0.8:

• FSM transitions to a degraded state
• Design adaptation is triggered