Endowing nonlinear systems with safe behavior is increasingly important in modern control. This task is particularly challenging for real-life control systems that operate in dynamically changing environments. This article develops a framework for safety-critical control in dynamic environments, by establishing the notion of environmental control barrier functions (ECBFs). Importantly, the framework is able to guarantee safety even in the presence of input delay, by accounting for the evolution of the environment during the delayed response of the system. The underlying control synthesis relies on predicting the future state of the system and the environment over the delay interval, with robust safety guarantees against prediction errors. The efficacy of the proposed method is demonstrated by a simple adaptive cruise control (ACC) problem and a more complex robotics application on a Segway platform.

Abstarct: This work presents a theoretical framework for the safety‐critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay‐free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced, to attain formal safety guarantees by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples.

In this contribution, heterogeneous connected vehicle systems, that include human-driven as well as connected automated vehicles, are investigated. The reaction time delay of human drivers as well as the communication and actuation delays of connected automated vehicles is incorporated in the model. Saturations due to the speed limit and limited acceleration capabilities of the vehicles are also taken into account. The arising nonlinear delayed system is studied using analytical and numerical bifurcation analysis. Stability analysis is used to identify regions in parameter space where oscillations arise due to loss of linear stability of the equilibrium. Moreover, with the help of numerical continuation, bistability between the equilibrium and oscillations is shown to exist due to the presence of an isola. It is demonstrated that utilizing long-range wireless vehicle-to-vehicle communication the connected automated vehicle is able to eliminate the oscillations and keep the traffic flow smooth.