Exact constraint aggregation with applications to smart grids and resource distribution

As hierarchical predictive control of large-scale distributed systems grow in complexity, it eventually becomes necessary to consider aggregation of lower-level units into larger groups of units that can be handled efficiently at higher levels in the hierarchy. When aggregating similar units in this manner, it is advantageous if the aggregation maintains a certain degree of genericity, since the higher-level algorithms can then be designed with a higher degree of modularity. To achieve this goal, however, it is not only necessary to examine aggregation of models of the underlying units, but also the accompanying constraints. Constraint sets for rate- and storage volume-constrained units can often be represented as polytopes in high-dimensional Euclidean space; unfortunately, adding such polytopic sets in higher dimension than 2 has so far been considered a combinatorial problem. In this paper, we present a novel method for computing such polytopic constraint sets for integrating units, which achieves a much lower computational complexity than previous results. The concept is demonstrated via simulations of a smart grid control scenario.