CSR---EHS: Embedded Viability Computing

在过去的15年中，生存理论在最优控制、微分对策和混合系统可达性等领域取得了重大的理论成就。该理论的当前状态使得嵌入式计算也能取得重大突破。该项目侧重于开发新的集值数值分析方案及其在特定应用（嵌入式）平台上的实现。本文主要研究三个关键问题：(1)生存集计算的高阶数值格式。这为最优控制问题的数值解提供了更快的收敛速度。(2)离散映射的形式化验证算法。这使得创建最优控制策略直接适用于用测量数据阵列而不是代数函数描述的问题。(3)集值最优控制算法。这些方法为经典控制技术无法纳入状态约束的问题提供了全局最优解。一个通用的计算核心正在被开发、定制并嵌入到软件和硬件平台中，用于土木和环境工程以及空中交通管制的两个关键应用。这被集成到一个正在开发的硬件平台：一个有源拉格朗日传感器网络（传感器安装在有源漂移器上，跟随环境流动）。该网络的目标是跟踪水中的分布特征（盐锋和浊度羽流）。驱动应用是河口环境的混合监测。该网络将部署在加利福尼亚州的圣华金-萨克拉门托三角洲。在NASA艾姆斯，该网络正在与FACET软件进行接口，目的是帮助空中交通管制员在恶劣天气条件下优化风路线决策。

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.