Optimal design of control strategies for large-scale dynamics

供水管网的损耗约占全球水浪费的25%-50%，而电网系统的故障会导致供水中断，造成严重后果。作为对系统改进工业流程和资源管理的惊人追求的回应，数学界和工程界对优化流程和决策战略的兴趣在过去几十年里有了相当大的增长。在这个方向上，研究针对复杂动力学的强大而灵活的控制策略变得至关重要。这种理论见解与计算方法令人印象深刻的进步相结合，允许处理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被应用于通过可再生能源生产电力、在电化学超级电容器中储存以及控制用户和供应商网络上的公用事业分配，同时考虑到供需双方的随机影响。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的管理，提供量身定制的决策支持系统，能够应对我们社会必须面临的日益困难的挑战。从这个角度来看，拟议的研究计划旨在探索由发展偏微分方程控制的系统所带来的机会和挑战，其中控制以非线性的方式作用于系统。这类问题在大规模随机控制系统的统计方法中自然而然地出现。特别令人感兴趣的是控制器只能访问系统状态的部分测量的情况。在这种情况下，至关重要的是调查系统的结构属性，以弥补对系统某些组件的观察不足。为了实现这一目标，有必要发展新的解析和数值方法来设计由偏微分方程组描述的大系统的闭环控制策略。这一目标要求将非线性系统控制理论、动力系统最优化和渐近行为的不同方法与统计理论和概率论、数据收集和基于模型的强化学习方法的创新方法相结合，并最终应用这些新的见解来建立快速可靠的数值格式，通过计算模拟来预测所考虑的大规模模型的行为。

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.