Robust Control Barrier Functions for Nonlinear Control Systems with Uncertainty: A Duality-based Approach

TL;DR

This paper introduces a duality-based method for designing robust controllers for nonlinear systems with uncertainties, utilizing novel control barrier functions and data-driven parameter set reduction to ensure safety and stability.

Contribution

It proposes new robust control barrier and Lyapunov functions combined with an online data-driven approach for uncertainty reduction in nonlinear control systems.

Findings

Successfully guarantees safety and stability in numerical examples.

Reduces conservativeness of uncertainty bounds through online data collection.

Demonstrates effectiveness of the duality-based approach in uncertain nonlinear control.

Abstract

This paper studies the design of controllers that guarantee stability and safety of nonlinear control affine systems with parametric uncertainty in both the drift and control vector fields. To this end, we introduce novel classes of robust control barrier functions (RCBF) and robust control Lyapunov functions (RCLF) that facilitate the synthesis of safety-critical controllers in the presence of parametric uncertainty using quadratic programming. Since the initial bounds on the system uncertainty may be highly conservative, we present a data-driven approach to reducing such bounds using input-output data collected online. In particular, we leverage an integral set-membership identification algorithm that iteratively shrinks the set of possible system parameters online and guarantees stability and safety during learning. The efficacy of the developed approach is illustrated on two numerical examples.