Scalable control for large-scale networked systems with input saturation constraint using chordal decomposition

In this paper, the scalable control of large-scale networked systems(LSNSs) with input saturation constraints is studied using choral decomposition. Firstly, in order to more effectively address the control requirements of complex systems and reduce the communication load, the modeling of LSNSs with different plant and communication topologies is constructed on an undirected graph. Subsequently, the chordal decomposition theorem was employed to establish a set of linear matrix inequalities (LMIs) over maximal cliques, with the objective of ensuring the mean-square asymptotic stability of LSNSs with input saturation constraints. Additionally, a design methodology was proposed for the design of the $ \mathcal {H}_{\infty } $ H∞ scalable controllers, which ensures that the controllers of the maximal clique to which it belongs and the controllers of neighbouring maximal cliques are updated only when plugging-in or plugging-out subsystems. Furthermore, the proposed approach offers significant advantages in terms of reduced computational complexity and increased privacy. Finally, the effecyiveness of the proposed scalable control approach is validated by analyzing microgrids.