Resolving large-scale control and optimization through network structure analysis and decomposition: A tutorial review

Decomposition is a fundamental principle of resolving complexity by scale, which is utilized in a variety of decomposition-based algorithms for control and optimization. In this paper, we aim to give a tutorial review of the following aspects: (i) how to decompose a network representing a control or optimization problem according to its latent block structure, (ii) how decomposition is determined for distributed control, and (iii) how optimization problems are solved under decomposition. Directions for further developing decomposition methods and decomposition-based control and optimization algorithms are also discussed.