Robust Adaptive Discrete-Time Control Barrier Certificate

TL;DR

This paper introduces a robust adaptive control method for discrete-time systems that uses Control Barrier Functions to ensure safety despite uncertainties and disturbances, with real-time implementation and theoretical guarantees.

Contribution

It establishes a discrete-time barrier function certificate for online parameter estimation, enabling safe adaptive control without knowing true system parameters.

Findings

Guarantees positive invariance of the safe set under disturbances.

Allows separate design of parameter estimation and safety filter.

Demonstrates real-time safe control for uncertain discrete-time systems.

Abstract

This work develops a robust adaptive control strategy for discrete-time systems using Control Barrier Functions (CBFs) to ensure safety under parametric model uncertainty and disturbances. A key contribution of this work is establishing a barrier function certificate in discrete time for general online parameter estimation algorithms. This barrier function certificate guarantees positive invariance of the safe set despite disturbances and parametric uncertainty without access to the true system parameters. In addition, real-time implementation and inherent robustness guarantees are provided. The proposed robust adaptive safe control framework demonstrates that the parameter estimation module can be designed separately from the CBF-based safety filter, simplifying the development of safe adaptive controllers for discrete-time systems. The resulting safe control approach guarantees that the system remains within the safe set while adapting to model uncertainties, making it a promising strategy for discrete-time safety-critical systems.