Optimal Policy for Integration of Automated Vehicles into the Auto Market: A Control-Theoretic Perspective

With the advent of emerging technologies, such as 5G network, wireless communications, among many others, automated vehicles (AVs) are expected to come into the existing auto market in the foreseeable future. It is anticipated that there will be a transitional period when legacy vehicles (LVs) are being replaced gradually by AVs before AVs take up a full penetration in the auto market. As a result, these two types of vehicles will inevitably coexist during this period experiencing an interactive temporal evolution in terms of their market shares. Inspired by the well-known Lotka-Volterra equations, we develop a dynamic model capable of capturing precisely such temporal evolution. A discrete choice model is constructed and incorporated into the dynamic model to describe the likelihood of choosing AVs and LVs. The average price of AVs is assumed to be regulatable, and is considered, together with the amount of investment in AV-specific transportation infrastructure, as control (decision) variables to ensure a desired gradual integration of AVs into the auto market subject to practical constraints. Further, a Meyer problem is formulated with the objective of reaching a desired target, i.e., a specific market penetration rate (MPR) of AVs, at the end of the planning period. Using the Pontryagin's minimum principle (PMP), the formulated optimal control problem is solved giving the temporal AV integration policy which allows for appropriate regulations of the average AV price and for adjustments of the amount of investment in AV-specific infrastructure. A series of numerical results is presented to show the effectiveness of the proposed approach. Since the dynamic model is general and the control inputs, i.e., the average AV price and amount of investment in infrastructure, are easy to implement, it is believed that the procedures presented in this paper will provide significant insights, for government agencies, into developing long-term strategic planning policies in the era of AVs.