Robust Adaptive Discrete-Time Control Barrier Certificate

TL;DR

The paper tackles safety guarantees for discrete-time systems facing disturbances and parametric uncertainty by developing a robust adaptive safe-control framework based on Discrete-Time Control Barrier Functions (DT-CBFs). It decouples online parameter estimation from the safety filter, enabling modular design, and introduces an online input condition that yields safe inputs without knowing the true parameters. A robust adaptive CBC is derived, along with a causal, set-based estimation scheme (set-membership/RLS) and a practical safety-filter implementation. The approach is demonstrated on an adaptive cruise control example, showing maintained safety and improved responsiveness compared to baseline adaptive MPC variants, thereby enabling safety-critical operation in data-driven, sampled-data contexts.

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.

Figures (8)

• Figure 1: Sketch of (a) adaptively robustified safe sets, and (b) the safety filter projection when the nominal input is unsafe.
• Figure 2: Diagram of the proposed safe control approach for the adaptive cruise control problem using robust adaptive discrete-time control barrier functions.
• Figure 3: $\mathtt{EST}$ performance. The shaded area is the min-max envelope encompassing different disturbance realizations.
• Figure 4: Comparison of adaptive MPC with robust adaptive CBF-based safety filter (aMPC-raCBF), MPC with worst-case robust CBF-based safety filter (MPC-rCBF), adaptive MPC (aMPC), and robust adaptive MPC (raMPC) kohler2021robust. The shaded area is the min-max envelope encompassing different disturbance realizations.
• Figure :

Theorems & Definitions (13)

• Remark 1
• Definition 1: Robust safety
• Remark 2
• Definition 2: Robust CBF
• Definition 3: Timed robust safety
• Definition 4: Robust adaptive CBF
• Remark 3
• Remark 4
• Remark 5
• Remark 6