Parameter Drift Instability in Disturbance-Free Adaptive Systems

Adaptive identification and control algorithms can exhibit local instability when certain ideal assumptions, such as satisfaction of SPR conditions, are violated. However, recent conjectures suggest that due to a “self-stabilization” mechanism, global boundedness may still hold despite local instabilities. We present counterexamples to these conjectures, showing that self stabilization is bypassed via “hidden” unbounded parameter drift. Although parameter drift instability is known to occur in adaptive systems with disturbances, concrete examples are given to show that unbounded drift can also occur in the disturbance-free case when SPR conditions are violated.