Adaptive Control with Sparse Identification of Nonlinear Dynamics
This work addresses control of uncertain nonlinear systems for robotics or aerospace applications, but it is incremental as it combines existing techniques like sparsity promotion and integral concurrent learning.
The paper tackles the problem of controlling uncertain nonlinear systems by developing an online adaptation law that promotes sparsity in parameter identification, resulting in ultimately bounded closed-loop trajectories as verified through simulations.
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.