A Parallelizable Algorithm for Stabilizing Large Sparse Linear Systems With Uncertain Interconnections

Abstract

This paper proposes a new method for permuting sparse matrices into an upper block triangular from. The algorithm is highly parallelizable, which makes it suitable for large-scale systems with uncertain interconnection patterns. In such cases, the proposed decomposition can be used to develop flexible decentralized control strategies that produce a different gain matrix whenever the configuration changes. Applications to interconnected microgrids and supply and demand networks are provided to illustrate the versatility of the proposed approach.INDEX TERMS Large-scale systems, reconfigurable interconnections, uncertainty, decentralized control, sparse matrices, block triangular structure, parallel graph theoretic decompositions.

Stochastic Distributed Control for Arbitrarily Connected Microgrid Clusters

“…Note that this will be the case regardless of how the microgrids are actually numbered-for stability purposes, it suffices to recognize that a permutation that produces the structure in (17) exists for every possible energy exchange pattern. A more general scenario where existence is not guaranteed is described in [30]. In this case, it is necessary to use an efficient decomposition algorithm that can determine an appropriate decentralized control law.…”