Optimal design of control strategies for large-scale dynamics

供水管网的损失约占全球水浪费的25-50%，而电网系统的故障会导致服务中断，并产生严重后果。在过去的几十年里，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和决策策略的优化的兴趣大大增加。在这个方向上，研究强大而灵活的复杂动力学控制策略变得至关重要。将这些理论见解与计算方法的令人印象深刻的进步相结合，可以处理在几个工程应用的建模和控制中出现的大规模问题类的优化。例如，在本研究框架内开发的分析方法和计算工具将应用于通过可再生能源、电化学超级电容器的存储以及在用户和供应商网络上控制公用事业分配的建模，同时考虑到供需中的随机效应。长期目标是提供严谨的工具，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，提出的研究计划旨在探索由偏微分演化方程控制的系统控制所带来的机遇和挑战，其中控制以非线性方式作用于系统。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值的情况。在这种情况下，研究系统的结构特性是至关重要的，它可以弥补对系统某些组成部分缺乏观察的不足。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描述的大尺度动力学的闭环控制策略。这一目标需要结合非线性系统控制理论、动态系统优化和渐近行为的不同方法，以及统计理论和概率论、数据收集和基于模型的强化学习方法的创新方法，最后应用这些新见解建立快速可靠的数值方案，通过计算模拟来预测所考虑的大尺度模型的行为。

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.