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

2025-07-17

AI Summary

This paper addresses robust control of nonlinear systems with state–input coupled uncertainties and no prior model assumptions. We propose a novel framework integrating differential contraction theory with data-driven prediction. Our key contributions are: (i) the first incorporation of conformal prediction to quantify uncertainty’s impact on contraction conditions, yielding finite-time, exponentially convergent probabilistic bounds on trajectory tracking error—without distributional assumptions; and (ii) the definition and construction of a probabilistic robust control invariant (PRCI) tube, enabling distributionally robust motion planning. The method imposes no assumptions on uncertainty structure or predictor form, relying solely on online data for estimation. Numerical experiments validate the exponential boundedness of tracking error and confirm the PRCI tube’s efficacy in guaranteeing high-probability safety.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Planning under Uncertainty

Application Category

• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• Robust control for nonlinear systems with state and control-dependent uncertainty
• Data-driven uncertainty prediction without structural assumptions
• Distribution-free probabilistic guarantees for trajectory tracking error

Innovation

• Data-driven uncertainty prediction for robust control
• Conformal prediction for probabilistic error guarantees
• Probabilistically robust control invariant tube design