Robust Safety-Critical Control for Input-Delayed System with Delay Estimation

This paper proposes a Control Barrier Function (CBF)-based delay adaptive controller design to accomplish robust safety in the presence of unknown but bounded constant input delay. To this end, we first estimate the input delay by using a gradient descent method minimizing the discrepancy between the current state and the estimated state. Then, we establish the state prediction feedback with the estimated input delay, which is leveraged to attenuate the effect of the input delay. However, due to the error between the true delay and the estimated delay, there is a state prediction error that leads to violations of safety if we use the normal CBFs. To remedy this, we use ideas from Measurement Robust Control Barrier Functions (MRCBFs) that enforce the robust safety constraint against the state prediction error. Specifically, we bound the state prediction error in connection with the input delay estimation error and incorporate the worst case error bound into the safety constraint. The proposed method is verified in the simulations under the connected automated vehicles scenario.