Adaptive Control with Sparse Identification of Nonlinear Dynamics

Abstract

This paper develops a sparsity-promoting integral concurrent learning (SP-ICL) adaptation law for a linearly parametrized uncertain nonlinear control-affine systems. The unknown parameters are learned using ICL with sparsity-promoting ${\ell }_1$ regularization. The use of ${\ell }_1$ regularization for sparsity promotion is common in system identification and machine learning; however, unlike existing approaches, this paper develops an online parameter update law that integrates the regularization penalty with ICL via sliding modes. We show via non-smooth Lyapunov analysis that the trajectories of the closed-loop system are ultimately bounded under the SP-ICL update law. Simulations verify the effectiveness of the sparsity penalty in the SP-ICL update law on recovering sparse dynamics during trajectory tracking.

arXiv commentAccepted for presentation in the 65th IEEE Conference on Decision and Control (CDC) 2026