Compositional synthesis of abstractions for infinite networks

最近在计算、廉价的分布式传感和大规模数据管理方面的进展为新的应用创造了潜力，其中大量分散的代理需要为了一个共同的目标而受到监管。例如，在智能城市领域，基于廉价的个人通信、车对车通信和部署大量传感器的全市交通控制可以向节能和环境友好的交通概念迈出重要一步。有效控制这种大型、分散的系统的愿景需要可扩展的工具，这些工具能够处理不确定和时变数量的参与子系统、有限的通信以及严格的安全规范。不正确配置的代价以及安全和安保问题需要用于复杂系统的验证和综合的自动化和可证明是正确的技术。此外，新出现的应用需要复杂的控制目标，这远远超出了经典控制理论中追求的标准目标。例如，一个复杂的目标是调整交通信号灯，以使拥堵最小化，并确保高速公路吞吐量保持在最低阈值以上。控制目标的复杂性、参与主体的数量和问题的复杂性要求通过融合计算机科学和控制理论的思想来系统地、自动地综合可证明是正确的控制器的方法。特别是，基于构造的正确性自动验证和综合最初是为了描述和验证软件和硬件系统的正确行为而开发的，它提供了一个严格的框架来有效地解决上述问题。基于符号模型(或有限抽象)的自动控制器综合的研究近年来取得了重大进展。然而，对于大规模且可能是无限维的情况，缺乏一种有效的方法。由于构建符号模型的计算复杂性通常随状态空间的维度呈指数级增长，因此对于大规模系统而言，暴力方法是不可行的。相反，我们建议使用系统结构来推导基于耗散性或小增益论证的大系统的方法，该项目旨在为由可数无限个动态耦合子系统组成的系统的分布式符号控制发展一个严格的数学框架。我们提出的方法将保持网络结构，以便于分布式控制设计。理论结果的有效性将通过在交通网络中的应用来验证。

Recent advances in computing, cheap distributed sensing and large-scale data management have created the potential for new applications, in which large numbers of dispersed agents need to be regulated for a common objective. In the domain of Smart Cities, for instance, city-wide traffic control based on cheap personal communication, car-to-car communication and the deployment of numerous sensors can provide a major step towards energy-efficient and environmentally friendly traffic concepts. The vision of efficiently controlling such large, dispersed systems requires scalable tools that are capable of handling uncertain and time-varying numbers of participating subsystems, limited communication, as well as stringent safety specifications. The costs of incorrect configuration as well as safety and security concerns require automated and provably correct techniques for the verification and synthesis of complex systems. Moreover, emergent applications necessitate sophisticated control objectives, which go well beyond standard goals pursued in classic control theory. For instance, a complex objective is to adjust the traffic lights such that congestion is minimized and freeway throughput is ensured to remain above a minimum threshold. The complex nature of control objectives, number of participating agents, and the complexity of the problem call for methods on systematic, automated synthesis of provably correct controllers by merging ideas from computer science and control theory. In particular, correct-by-construction automated verification and synthesis, which were originally developed for specifying and verifying the correct behavior of software and hardware systems, provide a rigorous framework to efficiently address the above issues.The study of automated controller synthesis based on symbolic models (or finite abstractions) has seen major advances in recent years. However, an efficient approach to the large-scale and possibly infinite-dimensional case is missing. As the computational complexity of constructing symbolic models often scales exponentially with the dimension of the state space, a brute force approach to large-scale systems is not feasible. Instead, we propose to use system structure to derive methods for large-scale systems based on dissipativity or small-gain arguments.This project aims to develop a rigorous mathematical framework for distributed symbolic control of systems composed of a countably infinite number of dynamically coupled subsystems. Our proposed methods will preserve the structure of the network in order to facilitate distributed control design. The effectiveness of the theoretical results will be verified by applications to trafficnetworks.