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

We introduce a novel class of accelerated data-driven concurrent learning algorithms. These algorithms are suitable for the solution of high-performance system identification and parameter estimation problems with convergence certificates in settings where the standard persistence of excitation condition is difficult to guarantee or verify a priori. To achieve (uniform) fast and fixed-time convergence, the proposed algorithms exploit the existence of information-rich data sets, as well as certain non-smooth regularizations of dynamical systems that generate a family of non-Lipschitz systems modeled as data-driven ordinary differential equations (DD-ODEs) and/or data-driven hybrid dynamical systems (DD-HDS). In each scenario, we provide stability and convergence certificates via Lyapunov theory. Moreover, to illustrate the practical advantages of the proposed algorithms, we consider an online estimation problem in Lithium-Ion batteries where the satisfaction of the persistence of excitation condition is in general difficult to guarantee.