A graph-based approach for optimal control in safest routing

Abstract

The subject of this study is a discrete-time routing control system whose objective is to nd controls that enable the system to start at a given point and converge to a prescribed target, while remaining within the region. Additionally, a safety analysis is performed for the routing system, where a safety degree is associated with each point. The aim is not only to route the system but also to maximize the minimum safety along the route. The concept of a safety path is introduced, representing a trajectory that avoids potential hazards and minimizes risks in the system's operation. The main objective is to compute an approximation of the optimal value function, which maximizes the minimum safety along the routing system. This is performed by a graph-based approach.