Adaptive Control with Sparse Identification of Nonlinear Dynamics

TL;DR

This paper introduces a new adaptive control law that promotes sparsity in identifying nonlinear system dynamics using integral concurrent learning with $$ regularization, ensuring bounded trajectories.

Contribution

It develops an online parameter update law combining $$ regularization with ICL via sliding modes, enhancing sparse dynamics recovery in nonlinear control systems.

Findings

The SP-ICL law effectively promotes sparsity in parameter estimates.

Simulations demonstrate accurate recovery of sparse dynamics during tracking.

The approach guarantees ultimate boundedness of system trajectories.

Abstract

This paper develops a sparsity-promoting integral concurrent learning (SP-ICL) adaptation law for a linearly parametrized uncertain nonlinear control-affine system. 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. Using the SP-ICL update law, we show via non-smooth Lyapunov analysis that the trajectories of the closed-loop system are ultimately bounded. Simulations verify the effectiveness of the sparsity penalty in the SP-ICL update law on recovering sparse dynamics during trajectory tracking.