Persistence of excitation of adaptive control schemes without continually disturbed controls

This paper treats the subject of the persistence of excitation of the states of a convergent adaptive control scheme. Recent work has shown that a persistently exciting (or continually disturbed) set point sequence guarantees this property of the states but can degrade the controller´s performance. The investigation here examines to what extent the system measurement noise can perform the function of exciting the states of the closed loop system.