Eindhoven University of Technology (TU/e)
Here, you find information on research activities, publications, and members within the project:
Conservation laws are evolution equations that describe fundamental laws of nature and are therefore central to our understanding of the physical world. Moreover, a mathematical handle on these equations would allow for the design of mechanisms to be used in controlling real-world systems. An important subclass of conservation laws is that of nonlocal transport equations with nonlinear mobility (NTNs). They commonly arise as large population limits of complex phenomena manifested in interacting systems that exist at different scales of organization—from subatomic entities in physical and biological processes to planetary systems. NTNs are also used on network structures to study, e.g., transportation and information networks, and supply chains, with the intent of optimizing said networks.
Despite the abundance of mathematical tools available for studying specific subclasses of conservation laws, these tools are not directly applicable to NTNs. For this reason, new tools have been developed in the past years, and are still being developed, to analyze them. Based on recent works on NTNs, and on a discrete-to-continuum approach for optimal control, this project proposes a novel and mathematically justified framework for studying optimal control problems for NTNs and for NTNs on networks. This new framework not only unifies various optimal control theories for conservation laws but also enables the development of efficient numerical algorithms for the design of control mechanisms, such as smart traffic light controls for transportation networks.