Minimizing Conservatism in Safety-Critical Control for Input-Delayed Systems via Adaptive Delay Estimation

Input delays affect systems such as wirelessly connected autonomous vehicles, and may lead to safety violations. One promising way to ensure safety in the presence of delay is to employ control barrier functions (CBFs), and extensions thereof that account for uncertainty: delay adaptive CBFs (DaCBFs). This paper proposes an online adaptive safety control framework for reducing the conservatism of DaCBFs. The main idea is to reduce the maximum delay estimation error bound so that the state prediction error bound is monotonically non-increasing. To this end, we first leverage both delay estimation and the estimation error bound of a disturbance observer to derive an upper bound on the current state prediction error from the previous state. Second, we design two nonlinear programs to update the maximum delay estimation error bound satisfying the obtained state prediction error bound previously and afterwards update the maximum error bound of the future state prediction used in DaCBFs. The proposed method ensures the maximum state prediction error bound with the delay estimation is monotonically non-increasing, yielding less conservatism in DaCBFs. We verify the proposed method in an automated connected truck application, showing that the proposed method reduces the conservatism of DaCBFs.