Adaptive Robust Quadratic Programs using Control Lyapunov and Barrier Functions

TL;DR

This paper introduces an adaptive robust quadratic programming control framework that uses control Lyapunov and barrier functions to handle nonlinear systems with uncertainties, ensuring safety and improved estimation accuracy.

Contribution

It proposes a novel adaptive estimation law for uncertainties and integrates it into a robust QP framework to enhance safety and reduce conservatism in uncertain nonlinear systems.

Findings

Effective uncertainty estimation with error bounds

Reduced conservatism by decreasing sampling time

Validated approach through simulations on adaptive cruise control

Abstract

This paper presents adaptive robust quadratic program (QP) based control using control Lyapunov and barrier functions for nonlinear systems subject to time-varying and state-dependent uncertainties. An adaptive estimation law is proposed to estimate the pointwise value of the uncertainties with pre-computable estimation error bounds. The estimated uncertainty and the error bounds are then used to formulate a robust QP, which ensures that the actual uncertain system will not violate the safety constraints defined by the control barrier function. Additionally, the accuracy of the uncertainty estimation can be systematically improved by reducing the estimation sampling time, leading subsequently to reduced conservatism of the formulated robust QP. The proposed approach is validated in simulations on an adaptive cruise control problem and through comparisons with existing approaches.