Discrete-time, normalized recursive least squares based concurrent learning for online function approximation

Abstract

Concurrent learning (CL) leverages strategic data collection and usage to deliver effective learning under conditions less demanding than persistency of excitation. Using a linear-in-the-parameters model to approximate a general discrete-time (DT) uncertainty, we develop a DT normalized recursive least squares-based CL algorithm, thereby mixing CL and least squares. Our algorithm not only preserves the properties of the standard normalized recursive least squares algorithm for both structured and unstructured DT uncertainties, but it additionally yields convergence of the parameter error to the origin. This is achieved if a matrix composed of vectors in the function approximator’s regressor has as many linearly independent columns as the dimensions of the said vectors, a condition that can be monitored and realized online with exciting, rather than persistently exciting, vectors. Numerical simulations of our proposed algorithm, including its use when implementing an indirect adaptive controller for a class of nonlinear continuous-time and discrete-time plants, demonstrate its value.