Estimation and Control of Networked Distributed Parameter Systems: Application to Traffic Flow

Abstract

The management of large-scale transportation infrastructure is becoming a very complex task for the urban areas of this century which are covering bigger geographic spaces and facing the inclusion of connected and self-controlled vehicles. This new system paradigm can leverage many forms of sensing and interaction, including a high-scale mobile sensing approach. To obtain a high penetration sensing system on urban areas more practical and scalable platforms are needed, combined with estimation algorithms suitable to the computational capabilities of these platforms. The purpose of this work was to develop a transportation framework that is able to handle different kinds of sensing data (e.g., connected vehicles, loop detectors) and optimize the traffic state on a defined traffic network. The framework estimates the traffic on road networks modeled by a family of Lighthill-Whitham-Richards equations. Based on an equivalent formulation of the problem using a Hamilton-Jacobi equation and using a semi-analytic formula, I will show that the model constraints resulting from the Hamilton-Jacobi equation are linear, albeit with unknown integer variables. This general framework solve exactly a variety of problems arising in transportation networks: traffic estimation, traffic control (including robust control), cybersecurity and sensor fault detection, or privacy analysis of users in probe-based traffic monitoring systems. This framework is very flexible, fast, and yields exact results. The recent advances in sensors (GPS, inertial measurement units) and microprocessors enable the development low-cost dedicated devices for traffic sensing in cities, 5 which are highly scalable, providing a feasible solution to cover large urban areas. However, one of the main problems to address is the privacy of the users of the transportation system, the framework presented here is a viable option to guarantee the privacy of the users by design.