Partitioning for Large-Scale Systems: Sequential DMPC Design

Chapter 7, where the Shapley value has been studied, has also discussed a partitioning as a result of the power index [1]. On the contrary, this chapter is devoted to the development of a partitioning strategy. As it has been reviewed in Chap. 2, several partitioning methods have been discussed in literature for both particular and general cases, e.g., [2, 3, 4, 5, 6, 7, 8, 9], among others. More precisely, the main contribution presented in this chapter is a novel partitioning approach of a non-directed graph representing information sharing inspired by the Kernighan-Lin algorithm [10], considering four different objectives, i.e., to minimize the number of links connecting partitions, to minimize the difference of the size of partitions, to minimize the distance among elements composing each partition, and to minimize the amount of relevant information that connects different partitions, i.e., it is also considered how relevant the information that a link provides is. Furthermore, prioritization weights assign importance to each objective as desired. Most of the partitioning methods consider a graph representation, i.e., algorithms consider graphs associated to the dynamics of the system. Differently, this chapter proposes to generate a graph that describes the information dependence among variables considered in the control design. As an application to illustrate the advantages of the partitioning approach addressed by using an information representation instead of a dynamical-model representation, a large-scale water supply system is considered, and an MPC controller is designed. To this end, the information graph is computed in order to determine an appropriate partitioning by using the proposed algorithm.