# CAREER: Hierarchical Control for Large-Scale Cyber-Physical Systems

Many complex engineering systems involve interactions among a large number of agents with coupled dynamics and decisions due to their shared environment and resources. Such systems are often operated using a hierarchical architecture, where a coordinator determines some macroscopic control signal to steer the population to achieve a desired group objective while respecting local preferences and constraints for individual agents. Examples include electricity demand response programs, ground and air transportation systems, data center power management, robotic networks, among others. The goal of this project is to establish new control and game theoretic foundations, along with numerical algorithms, to enable formal and scalable design of hierarchical population control systems. In contrast to the existing literature that primarily focuses on static strategic agents, this project will consider both strategic and non-strategic agents with nontrivial dynamics. So far, we have obtained the following main results. (i) Non-strategic CPS agent is typically associated with a predefined local response rule. We have proposed a hybrid system model to describe individual agent dynamics, and developed a stochastic hybrid system model to capture of the aggregate population dynamics. A novel approach based on abstraction of stochastic hybrid systems (SHS) has been developed to solve the hierarchical population control problem. (ii) For strategic agents, we have obtained new theoretical results on mean-field games. Different from many results in the literature, we studied mean-field games from an optimization perspective. We show that an important class of mean-field games is strongly connected (sometimes equivalent) to a corresponding optimization problem in vector space. Such connection has profound theoretical implications, and can be used to significantly simplify the analysis and computation of mean-field equilibrium of the population. This is an important step towards an efficient solution of the hierarchical population control problem with strategic agents.

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