A RESULT ON EXPONENTIAL TRACKING ERROR CONVERGENCE AND PERSISTENT EXCITATION

Conditions are investigated for exponential convergence of the trackin g error in feedforward adaptive systems having insufficient excitation . Particular attention is paid to the adaptive gradient algorithm with periodic excitation in the overparameterized case. A main result is t hat for a bounded periodic regressor, the tracking error converges exp onentially without regard to parameter convergence or to the degree of overparameterization. These results weaken the persistent excitation (PE) conditions and parameter convergence renditions generally conside red necessary to ensure exponential tracking convergence in this class of systems.