Learned Lyapunov Shielding for Adaptive Control

TL;DR

This paper introduces a learned Lyapunov-based safety framework for adaptive control of Euler--Lagrange systems, combining neural networks, reinforcement learning, and a safety filter to improve stability and robustness.

Contribution

It develops a novel integrated approach with a learned Lyapunov function, residual policy, and physics-informed neural network, enabling safe adaptive control without online QP solvers.

Findings

Achieved 41% reduction in tracking error under nominal friction.

Demonstrated scalability on a 7-DOF robot with stable convergence.

Validated the safety filter's feasibility and robustness theoretically and empirically.

Abstract

We augment the Slotine--Li adaptive controller for Euler--Lagrange systems with three learned components: a structured-quadratic Lyapunov function \(V_\psi\) whose positive-definiteness follows from a Cholesky parameterization, a residual Soft Actor--Critic policy that adds bounded torque corrections to the analytic baseline, and a physics-informed neural network that estimates unmodeled dynamics. A closed-form safety filter, derived from the single affine constraint \(\dot V_\psi + \alpha V_\psi \le 0\), projects every policy output onto the safe set without requiring an online QP solver. We prove: global feasibility of the filter under a drift-decay condition on the control-degeneracy set; exponential stability under exact shielding, with a robust extension whose margin depends on the PINN approximation error; almost-sure convergence of the three-timescale policy--certificate--multiplier updates to a KKT point; and a PAC generalization bound for the certificate over compacts. On a 2-DOF manipulator with nonlinear friction and variable payload, the learned certificate accounts for most of the empirical gain: tracking error drops by 41\% on nominal friction and 24\% on aggressive friction at the centroid of the training distribution. A 7-DOF scalability study on a Franka Emika Panda confirms clean convergence of the full pipeline at industrial scale, identifies the conditions under which gains over exact model-based baselines should and should not be expected, and documents a warm-start pathology of the learned certificate that has practical implications for deployment.