Optimal design of control strategies for large-scale dynamics

大范围动力学控制策略的优化设计

• 批准号: RGPIN-2021-02632
• 负责人: Guglielmi, Roberto
• 金额: $ 1.31万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=743678
• 关键词: Optimal; design; control; strategies; large

Losses in Water Distribution Network account for about 25-50% of water waste worldwide, while faults in electrical grid systems cause disruption in the service with critical consequences. In response to the striking quest for a systematic improvement of industrial processes and management of resources, the interest of the mathematical and engineering communities towards the optimization of processes and decision-making strategies has considerably grown over the last few decades. In this direction, it becomes crucial to investigate powerful and flexible control strategies for complex dynamics. The combination of such theoretical insights with the impressive advances in computational methods allows to cope with the optimization of classes of large-scale problems, that appear in modeling and control of several engineering applications. For example, the analytical methods and computational tools developed in the framework of this research will be applied to model the production of electricity by means of renewable sources, the storage in electrochemical supercapacitors, and the control of the distribution of the utility over a network of users and suppliers, taking into consideration random effects in both supply and demand. The long-term goal is to provide rigorous tools to systematically support the optimization of industrial processes and the management of resources, delivering tailored decision support systems able to tackle the challenges of increasing difficulty that our society must face. In this perspective, the proposed research program intends to explore the opportunities and challenges given by the control of systems governed by partial differential equations of evolution, where the control acts on the system in a nonlinear manner. This class of problems appears in a natural way in a statistical approach to large-scale stochastic control systems. Of particular interest is the situation of a controller that has access to only partial measurements of the states of the system. In this circumstance, it is crucial to investigate structural properties of the system that may compensate for the lack of observation on some components of the system. In order to achieve this goal, it is necessary to develop new analytical and numerical methods to design control strategies in closed-loop form for large-scale dynamics described by partial differential equations. This objective requires to combine different methods from control theory of nonlinear systems, optimization and asymptotic behavior of dynamical systems, together with innovative approaches from statistical theory and probability, data collection and model-based reinforcement learning methods, and finally to apply these new insight to build fast and reliable numerical schemes to forecast by means of computational simulations the behavior of the large-scale models under consideration.

供水管网的损失约占全球水资源浪费的25-50%，而电网系统的故障会导致服务中断，并造成严重后果。为了响应对工业过程和资源管理的系统改进的惊人追求，数学和工程界对过程优化和决策策略的兴趣在过去几十年中大大增长。在这个方向上，它变得至关重要，研究强大而灵活的控制策略，复杂的动态。这种理论见解与计算方法的令人印象深刻的进步相结合，可以科普在几个工程应用的建模和控制中出现的大规模问题的优化。例如，在本研究框架内开发的分析方法和计算工具将用于模拟可再生能源的电力生产，电化学超级电容器的存储，以及用户和供应商网络上公用事业的分布控制，同时考虑到供应和需求的随机效应。长期目标是提供严格的工具，系统地支持工业流程的优化和资源管理，提供量身定制的决策支持系统，能够应对我们社会必须面对的日益困难的挑战。从这个角度来看，拟议的研究计划旨在探索的机会和挑战，由偏微分方程的演化，其中控制作用于系统的非线性方式控制系统。这类问题以一种自然的方式出现在大规模随机控制系统的统计方法中。特别令人感兴趣的是控制器的情况下，只有部分测量系统的状态。在这种情况下，至关重要的是调查系统的结构特性，可以弥补缺乏对系统的某些组件的观察。为了实现这一目标，有必要开发新的分析和数值方法来设计闭环形式的控制策略，用于由偏微分方程描述的大规模动态。这一目标需要将非线性系统控制理论、动力系统的优化和渐近行为的不同方法与统计理论和概率、数据收集和基于模型的强化学习方法的创新方法联合收割机结合起来，最后，应用这些新的见解，建立快速和可靠的数值方案，通过计算模拟预测的行为，大，正在考虑的模型。