Robust Adaptive Discrete-Time Control Barrier Certificate

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. Our approach demonstrates that, using the proposed robust adaptive CBF framework, 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 safety filter guarantees that the system remains within the safe set while adapting to model uncertainties, making it a promising strategy for real-world applications involving discrete-time safety-critical systems.