Constrained control of multi-input systems with distinct input delays

We consider the problem of enforcing safety in multi-input systems with distinct input delays via the use of Control Barrier Functions (CBFs). For systems with input delay(s), a popular approach for enforcing safety is the combination of a CBF designed for the delay-free system with state-predictors that compensate the input delays. Typically, this comes with the assumption that the system does not violate safety constraints before all input delays have been compensated and the system is fully under control. In this paper, we introduce two control approaches that enforce safety before all input delays have been compensated, whenever it is possible to do so. We do this by utilizing a robust CBF formulation that treats longer-delayed inputs as known disturbances when determining control effort for shorter delayed inputs. This formulation ensures that, whenever possible, a subset of input channels with shorter delays will be utilized for keeping the system in the admissible safe set before longer input delays have been compensated. The effectiveness of our approaches is demonstrated with two numerical examples.