Discrete-time indirect adaptive control of a class of single state systems using concurrent learning for parameter adaptation

We have previously showed that it is possible to achieve parameter identification of discrete-time structured uncertainties without requiring persistency of excitation when using Concurrent Learning. Instead, granted a less restrictive condition compared to that of persistency of excitation is verified, exponential convergence of parameter estimates to their true values ensues. The present study applies the previously developed discrete-time Concurrent Learning adaptation law within a control loop for discrete-time adaptive control of a discrete-time single-state plant containing structured uncertainties. Provided that the same condition as for the standalone estimation is met, we can prove exponential convergence of the tracking error and parameter error to zero without necessitating persistency of excitation.