Parameter identification in structured discrete-time uncertainties without persistency of excitation

Concurrent Learning has been previously used in continuous-time uncertainty estimation problems and adaptive control to solve the parameter identification problem without requiring persistently exciting inputs. Specifically selected past data are jointly combined with current data for adaptation. Here, we extend the parameter identification problem results of Concurrent Learning for structured uncertainties in the continuous-time domain to the discrete-time domain. Alike the continuous-time case, we show that, in discrete-time, a sufficient, testable on-line and less restrictive condition compared to persistency of excitation guarantees global exponential stability of the parameter error when using Concurrent Learning.