In the past 15 years, viability theory has enabled significant theoretical achievements in the areas of optimal control, differential games and hybrid systems reachability. The current state of the theory now enables significant breakthroughs in embedded computing as well. This project focuses on the development of novel set-valued numerical analysis schemes and their implementation on application-specific (embedded) platforms. The research addresses three key topics: (1) Higher order numerical schemes for the computation of viability sets. These provide faster convergence rates for numerical solutions of optimal control problems. (2) Formal verification algorithms on discrete maps. These enable the creation of optimal control strategies directly applicable to problems described with arrays of measured data rather than algebraic functions. (3) Set-valued optimal control algorithms. These provide globally optimal solutions for problems in which classical control techniques cannot incorporate state constraints.
A generic computational core is being developed, customized and embedded in software and hardware platforms used for two key applications in Civil and Environmental Engineering, and in Air Traffic Control. This is integrated to a hardware platform in development: an active Lagrangian sensor network (sensors mounted on active drifters which follow environmental flows). The goal of this network is to track distributed features in water (salt fronts and turbidity plumes). The driving application is the monitoring of mixing in estuarine environments. The network will be deployed in the San-Joaquin - Sacramento Delta in California. At NASA Ames, the network is being interfaced with the software FACET, with the goal of helping Air Traffic Controllers to optimize wind routing decisions in severe weather conditions.
