Learned Lyapunov Shielding for Adaptive Control

2026-05-07

AI Summary

This work addresses the problem of safe adaptive control for Euler–Lagrange systems subject to unmodeled dynamics and uncertainties. It proposes a closed-form safety filtering mechanism that obviates the need for online quadratic programming. The approach integrates Cholesky-parameterized quadratic Lyapunov functions, Soft Actor-Critic reinforcement learning, physics-informed neural networks (PINNs), and a Lyapunov derivative-based safety projection to enforce stability constraints and correct control inputs in real time. Theoretical analysis establishes the filter’s global feasibility, exponential stability, and KKT convergence of the underlying three-timescale algorithm, along with a generalization error bound for the learned certificates. Experimental results demonstrate a 41% reduction in tracking error under nominal friction and 24% under high friction on a 2-DOF manipulator, while tests on a 7-DOF Franka Panda platform confirm the method’s industrial-scale applicability and convergence.

Abstract

We augment the Slotine--Li adaptive controller for Euler--Lagrange systems with three learned components: a structured-quadratic Lyapunov function \(V_ψ\) 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 \(\dot V_ψ+ αV_ψ\le 0\), 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.

Problem

• adaptive control
• safety
• stability
• unmodeled dynamics
• Euler-Lagrange systems

Innovation

• Learned Lyapunov Shielding
• Physics-Informed Neural Network
• Adaptive Control
• Safety Filter
• Exponential Stability