Library-based adaptive observation through a sparsity-promotingadaptive observer

Andreu Cecilia, Ramon Costa-Castelló European Control Conference (2021) This paper proposes an adaptive observer for a class of nonlinear system with linear parametrization. The main novelty of the technique is that the regressor vector is considered to be unknown. Instead, a library of candidate nonlinear functions is implemented, which transforms the original parameter vector into a new one that is characterized by being sparse. In such problem, it is shown that standard adaptive observers cannot recover the original vector due to a lack of persistence of excitation. Instead, a parameter-adaptation with an implicit $l_1$ regularization is implemented. It is shown that this new observer can recover the parameter vector under standard assumptions of sparse signal recovery. The results are validated in a numerical simulation.