Planning, Operation, and Management of Automated Transportation Systems: A Control-Theoretic Approach

Abstract

With the advent of emerging technologies like 5G network and wireless communication, automated vehicles (AVs) are expected to become increasingly available to travelers, offering a vast amount of benefits, such as enhanced traffic stability, reduced energy consumption, and optimized parking space allocation, among many others. It is highly anticipated that there will be a transitional period of the the auto market as human-driven vehicles (HVs) are gradually replaced by AVs. Many opportunities and challenges are expected to emerge during this transitioning process. To better prepare a nation for the arrival of AVs, in this dissertation we aim to address interesting yet pressing problems arising from vehicle automation in the context of planning, operation, and management of future transportation systems from a control-theoretic perspective. In view of the inevitable coexistence of HVs and AVs during the transitioning period, we develop a continuous-time dynamical model to capture the interactive temporal evolution of the market share of these two types of vehicles. A discrete choice model is constructed and incorporated into the dynamical model for describing the likelihood of customers choosing HVs or AVs. To achieve a desired temporal integration of AVs into the auto market, monetary subsidies and investment in AV-specific infrastructure are considered as decision variables to promote the adoption of AVs. Further, an optimal control problem is formulated with the objective of achieving a desired market penetration rate (MPR) at the end of any given finite planning horizon, while minimizing the cost of AV subsidies and infrastructure investment. The time-dependent optimal AV integration policy is determined by solving the formulated optimization problem, allowing a government agency to subsidize AV purchases and invest in future transportation infrastructure in an adaptive manner. The proposed approach is observed to be effective and robust under various demand patterns, such as increasing, decreasing, and stochastic demands. A systematic cost-benefit analysis with sensitivity analysis is conducted to evaluate the desirability of AV integration. The promising results provide significant managerial insights for government agencies into developing long-term strategic planning policies for the integration of AVs. Although appropriate incentive policies could accelerate the adoption of AVs, the MPR is expected to remain relatively low in the next thirty years or so, resulting in a predominantly human-driven mixed traffic flow consisting of HVs and AVs. Uniform traffic flow has been shown to be unstable in certain flow regimes due to collective behavior of human drivers, causing the well-observed stop-and-go waves. These traffic waves can arise even in the absence of merges, bottlenecks, or lane changing, and likely result in more energy consumption and emissions. Taking advantage of vehicle automation, we develop an approach to smoothing unstable traffic flow via optimal control of a small proportion of AVs in a predominantly human-driven traffic flow. These controlled AVs act as mobile actuators in mixed-autonomy traffic without changing the way HVs normally operate. We develop a general framework to describe mixed traffic flow with its dynamics abiding by car-following principles. Based on this framework, we synthesize optimal feedback controllers for AVs with the objective of minimizing speed disturbance, thereby resulting in smoother traffic. Following the necessary conditions of optimality prescribed by the Pontryagin's minimum principle, we present a computational algorithm for determining the optimal AV control strategy. The general framework is further illustrated using the intelligent driver model (IDM) and optimal velocity with relative velocity (OVRV) model for HVs and AVs, respectively, to show the effectiveness of the proposed approach on traffic smoothing, as well as the improvement on vehicle fuel economy and emissions. While the optimal AV controller synthesized above is shown to be effective in smoothing unstable mixed traffic, its performance on improving traffic stability is yet to be proven analytically and car-following safety is ensured in a fairly conservative manner. To address these challenging issues, we synthesize appropriate feedback controllers for AVs leveraging nonlinear stability theory. Specifically, we are interested to analytically synthesize appropriate feedback controllers of AVs for smoothing nonlinear mixed traffic in its general functional forms, covering a broad class of deterministic car-following models commonly seen in the literature. Essentially, AVs are controlled to operate in such a way that they closely track a virtual speed profile, i.e., a subtler version of the disturbance resulting from the immediately preceding vehicle. Thus, traffic waves are reduced when propagating backward across controlled AVs. Based on the general functional form of car-following dynamics, we derive a class of effective additive AV controllers that are proven to be able to ensure convergence in speed tracking, leading to smoother traffic. In addition, a set of sufficient conditions is devised for guaranteeing car-following safety. Notably, unlike many existing studies the feedback controllers synthesized require only local traffic information without having to rely on high degrees of vehicle connectivity, and the rate of traffic smoothing is readily tunable, which is useful for practical implementation. The proposed approach is further illustrated with a theoretical IDM and commercially available adaptive cruise control (ACC) vehicles represented by a well-calibrated IDM. In spite of the benefits promised by AVs like enhancing traffic stability shown above, emerging AV technologies open a door for cyberattacks, where a select number of AVs are compromised to drive in an adversarial manner. This could result in a network-wide increase in traffic congestion and vehicle fuel consumption, degrading the performance of transportation systems. Hence, developing effective attack mitigation strategies for AVs is critically important as AVs gradually become a reality. To this end, we derive optimal feedback control law for AVs in the presence of cyberattacks. Notably, attacks are only assumed to have a bounded magnitude (for remaining stealthy) without being subject to any specific probability distribution, which is not only of theoretical interest but also relaxes the assumptions of prior studies. More importantly, to deal with lack of knowledge of malicious attacks, we, for the first time, formulate a min-max control problem to minimize the worst-case potential disturbance to traffic flow. Specifically, under the framework of mixed-autonomy traffic presented before we consider two types of cyberattacks on AVs, namely false data injection attack on sensor measurements and malicious attack on AV control commands. Further, we derive a set of necessary conditions of optimality for the min-max control problem, based on which an iterative computational algorithm is developed for determining the optimal control (driving) strategy of AVs in a decentralized manner. The effectiveness of the proposed approach is demonstrated via numerical simulation considering different levels of attack severity.