Decision Making for Connected and Automated Vehicles: A Max-Plus Approach

In this paper, a method to model the decision making system of Connected and Automated Vehicles (CAVs) is discussed. The method is based on an algebra different from the conventional, the so-called Max-Plus algebra. First, a literature-review on the application of Max-Plus algebra in different sectors is presented. Then, the Max-Plus linear system theory is applied to a high-level decision making system used for the lane reduction scenario of Connected and Automated Vehicles. In the conclusion of this work, Max-Plus linear system theory has been found to be a suitable method to describe high-level decision making systems that are foreseen to be more and more deployed with the disruptive shift towards vehicle automation. In fact, the Max-Plus approach gives a quantitative description of the high-level decision maker, which could then be analyzed and controlled with mathematical tools from control system theory. These tools are similar to the methods available for continuous/discrete time linear systems in control theory.