Conformal Contraction for Robust Nonlinear Control with Distribution-Free Uncertainty Quantification

TL;DR

This paper introduces a data-driven, distribution-free robust control framework for nonlinear systems that uses conformal prediction to provide probabilistic guarantees on system stability and motion planning without relying on explicit uncertainty models.

Contribution

It combines contraction-based control with conformal prediction to achieve distribution-free, probabilistic robustness guarantees for nonlinear control systems.

Findings

Successfully guarantees exponential boundedness of trajectories.

Demonstrates effective distributionally robust motion planning.

Validates approach through numerical simulations.

Abstract

We present a novel robust control framework for continuous-time, perturbed nonlinear dynamical systems with uncertainty that depends nonlinearly on both the state and control inputs. Unlike conventional approaches that impose structural assumptions on the uncertainty, our framework enhances contraction-based robust control with data-driven uncertainty prediction, remaining agnostic to the models of the uncertainty and predictor. We statistically quantify how reliably the contraction conditions are satisfied under dynamics with uncertainty via conformal prediction, thereby obtaining a distribution-free and finite-time probabilistic guarantee for exponential boundedness of the trajectory tracking error. We further propose the probabilistically robust control invariant (PRCI) tube for distributionally robust motion planning, within which the perturbed system trajectories are guaranteed to stay with a finite probability, without explicit knowledge of the uncertainty model. Numerical simulations validate the effectiveness of the proposed robust control framework and the performance of the PRCI tube.