Accelerated Concurrent Learning Algorithms via Data-Driven Hybrid Dynamics and Nonsmooth ODEs

We introduce a novel class of data-driven accelerated concurrent learning algorithms. Thesealgorithms are suitable for the solution of high-performance system identification and pa-rameter estimation problems withconvergence certificates, in settings where the standardpersistence of excitation (PE) condition is difficult to verifya priori. In order to achieve(uniform) fast convergence, the proposed algorithms exploit the existence of information-rich data sets, as well as certain non-smooth regularizations that generate a family ofnon-Lipschitz dynamics modeled as data-driven ordinary differential equations (DD-ODEs)and/or data-driven hybrid dynamical systems (DD-HDS). In each case, we provide stabilityand convergence certificates via Lyapunov theory. Moreover, to illustrate the advantages ofthe proposed algorithms, we consider an online estimation problem in Lithium-Ion batterieswhere the satisfaction of the PE condition is difficult to verify.