Optimization-based disjoint and overlapping epsilon decompositions of large-scale dynamical systems via graph theory

To address the complexity challenge of a large-scale system, the decomposition into smaller subsystems is very crucial and demanding for distributed estimation and control purposes. This paper proposes novel optimization-based approaches to decompose a large-scale system into subsystems that are either weakly coupled or weakly coupled with overlapping components. To achieve this goal, first, the epsilon decomposition of large-scale systems is examined. Then, optimization frameworks are presented for disjoint and overlapping decompositions utilizing bipartite graphs. Next, the proposed decomposition algorithms are represented for particular cases of large-scale systems using directed graphs. In contrast to the existing user-based techniques, the proposed optimization-based methods can reach the solution rapidly and systematically. At last, the capability and efficiency of the proposed algorithms are investigated by conducting simulations on three case studies, which include a practical distillation column, a modified benchmark model, and the IEEE 118-bus power system.