Adaptive Control with Sparse Identification of Nonlinear Dynamics

arXiv:2604.06338 · math.OC, cs.SY, eess.SY · Submitted 2026-04-07 · Read on arXiv

math.OC, cs.SY, eess.SY

Submitted: 2026-04-07

Updated: 2026-09-22

Comments: Accepted for presentation in the 65th IEEE Conference on Decision and Control (CDC) 2026

License: http://creativecommons.org/licenses/by/4.0/

The gist: This paper develops a sparsity-promoting integral concurrent learning (SP-ICL) adaptation law for a linearly parametrized uncertain nonlinear control-affine systems.

Terminology

Sparsity — 28× in this paper · explained in 4 episodes
Regularization — 18× in this paper · explained in 3 episodes
Closed-Loop System — 7× in this paper · explained in 4 episodes
Adaptation — 6× in this paper · explained in 1 episode
System Identification — 5× in this paper · explained in 3 episodes
F1 Score — 4× in this paper · explained in 3 episodes
Accuracy — 3× in this paper · explained in 1 episode
Lyapunov function — 2× in this paper · explained in 2 episodes
Active Learning — 1× in this paper · explained in 6 episodes
Consistency — 1× in this paper · explained in 3 episodes
Convergence Guarantees — 1× in this paper · explained in 3 episodes
Fidelity — 1× in this paper · explained in 2 episodes

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 1 regularization. The use of 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.

Terminology

Abstract

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