Gradient-Based Discrete-Time Concurrent Learning for Standalone Function Approximation

When using standard learning techniques for uncertainty approximation, persistently exciting inputs are necessary in order to achieve good parameter estimation. It has been shown in recent years that, through concurrent learning (CL), it is possible to achieve better learning without requiring persistency of excitation. We define good learning here by how well an uncertainty can be reconstructed given the estimated parameters. Most studies concerning CL have however been done in the continuous-time (CT) framework. While working with discrete-time (DT) structured uncertainties, we have shown in an earlier study that the concept of CL could be used to solve the parameter identification problem granted, much like in the CT domain, a less restrictive condition compared to that of persistency of excitation is verified. This paper furthers our fundamental study of CL in the DT framework while drawing comparisons with the traditional but fundamental gradient descent technique. As a main contribution, via formal derivations, we present a generalized gradient-based CL motivated DT algorithm for online approximation of both DT structured and unstructured uncertainties. Numerical simulations are provided to show how well the designed algorithm leverages memory usage to achieve better learning.