Concurrent learning for convergence in adaptive control without persistency of excitation

We show that for an adaptive controller that uses recorded and instantaneous data concurrently for adaptation, a verifiable condition on linear independence of the recorded data is sufficient to guarantee exponential tracking error and parameter error convergence. This condition is found to be less restrictive and easier to monitor than a condition on persistently exciting exogenous input signal required by traditional adaptive laws that use only instantaneous data for adaptation.