Log-Domain Adaptive Control with Lyapunov Stability Guarantees: A Model-Free Approach for UAV Attitude Control

This paper introduces Log-domain Adaptive Control (LAC), a model-free gain-modulating wrapper that exploits the unused gain margin of a stabilizing baseline controller to suppress transient performance degradation. Unlike general-purpose adaptive controllers that attempt system identification or disturbance estimation, LAC operates as an event-driven gain modulation layer with three structural guarantees: (i) bounded, chatter-free gain evolution via log-domain adaptation with hysteresis switching, (ii) uniform ultimate boundedness under intermittent disturbances without requiring plant models, and (iii) fail-safe transparency—if adaptation is disabled, the system reverts to baseline performance. This paper establishes Lyapunov-based stability conditions and proves positive dwell-time existence that excludes Zeno behavior. The architectural constraints (stable baseline, intermittent disturbances, monotonic gain-performance relationship) are explicitly characterized, clarifying the regime in which gain modulation is provably safe, effective, and non-intrusive.