Discrete-time concurrent learning for system identification and applications: Leveraging memory usage for good learning

摘要

Literature on system identification reveals that persistently exiting inputs are needed in order to achieve good parameter identification when using standard learning techniques such as Gradient Descent and/or Least Squares for function approximation. However, realizing persistency of excitation in itself is quite demanding, especially in the context of on-line approximation and adaptive control. Much recently, Concurrent Learning (CL), through its utilization of memory (and, in that regard, quite similarly to human learning), has been shown to be able to yield good learning without the need to resort to persistency of excitation. For all intents and purposes, we refer to "good learning" throughout this work as the ability to reconstruct the function(s) being approximated well when using the estimated parameters.;The continuous-time (CT) domain literature on CL has seen the larger share of researches. For our part, we have focused on the discrete-time (DT) domain. Tough many systems can be modeled as CT systems, usually, controlling such systems, especially real-time (or, rather close to real-time), is done via the use of digital computers and/or micro-controllers, therefore making DT framework studies compelling.;We have shown that, similarly to the CT domain, granted a less restrictive CL condition compared to that of persistency of excitation is verified, analogous CL results to that obtained in the CT domain can also be achieved in the DT domain. Before incorporating and making use of the concept of concurrent learning in our studies, we thoroughly study the Gradient Descent and Least Squares techniques for function approximation and system identification of a dimensionally complex uncertainty, which, to the best our knowledge, is yet to be done in literature. Our main contributions are however the derivations of a DT Normalized Gradient (DTNG) based CL algorithm as well as a DT Normalized Recursive Least Squared (DTNRLS) based CL algorithm for approximation of both DT structured and DT unstructured uncertainties, while showing analytically that our devised algorithms guarantee good parameter identification if the aforesaid CL condition is met.;Numerical simulations are provided to show how well the developed CL algorithms leverage memory usage to achieve good learning. The algorithms are also made use of in two applications: the discrete-time indirect adaptive control of a class of discrete-time single state plant bearing parametric or structured uncertainties and the system identification of a robot.