Optimal design of control strategies for large-scale dynamics

点击翻译按钮获取中文摘要

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.