Towards Robust Data-Driven Control Synthesis for Nonlinear Systems with Actuation Uncertainty

TL;DR

This paper introduces a data-driven control synthesis method for nonlinear systems with actuation uncertainty, leveraging Control Certificate Functions to achieve stability and safety with data-dependent guarantees.

Contribution

It develops a convex optimization-based robust control framework using CCFs that handles model uncertainty and offers sample-efficient data collection strategies.

Findings

Validated in simulation with an inverted pendulum

Achieved stability and safety guarantees

Demonstrated robustness to actuation uncertainty

Abstract

Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework is nuanced data-dependent guarantees, which in principle can yield sample-efficient data collection approaches that need not fully determine the input-to-state relationship. This work serves as a starting point for addressing important questions at the intersection of nonlinear control theory and non-parametric learning, both theoretical and in application. We validate the proposed method in simulation with an inverted pendulum in multiple experimental configurations.