Distributed Data-Driven Decision Making in Uncertain Networked Systems with Applications in Smart Energy Systems

This dissertation aims to develop a rigorous distributed approach to decision making using scenario-based techniques for large-scale networks of interconnected uncertain dynamical systems (called agents). A scenario program is a finite-dimensional optimization problem in which an objective function is minimized under constraints that are associated with finitely many, independently and identically distributed (i.i.d.), scenarios of a random parameter. Theoretical and practical interest in scenario programs originates from the fact that these problems are typically efficiently solvable while being closely related to robust and chance-constrained programs. In the former, the constraint is enforced for all admissible random parameters, whereas in the latter, the constraint is enforced up to a given level of probability. However, finding solutions of the resulting large-scale scenario optimization problem for uncertain networked systems poses several difficulties, e.g., computational cost for a central control unit.
The main contribution of this dissertation is the design of a technique to decompose a large-scale scenario program into small-scale distributed scenario programs for each agent. Building on existing results in literature, we provide novel guarantees to quantify the robustness of the resulting solutions in a distributed framework. In this setting, each agent needs to exchange some information with its neighboring agents that is necessary due to the statistical learning features of the proposed setup. However, this inter-agent communication scheme might give rise to some concerns about the agents' private information. We therefore present a novel privatized distributed framework, based on the so-called differential privacy concept, such that each agent can share requested information while preserving its privacy. In addition, a soft communication scheme based on a set parameterization technique, along with the notion of probabilistically reliable set, is introduced to reduce the required communication burden. Such a reliability measure is incorporated into the feasibility guarantees of agent decisions in a probabilistic sense. The theoretical guarantees of the proposed distributed scenario-based decision making framework coincide with the centralized counterpart, however the scaling of the results with the number of agents remains an issue.