Distributed and Localized Covariance Control of Coupled Systems: A System Level Approach

This work is concerned with finiteâĂŚhorizon covariance steering for networked, discreteâĂŚtime stochastic linear systems with dynamically coupled subsystems, extending beyond existing work limited to decoupled ‘agents.’ We formulate a localized covariance-steering problem and, using the systemâĂŚlevel synthesis (SLS) framework, recast it as a convex optimization over system responses. After analyzing separability and applying a transformation for nonseparable objectives, we derive a distributed consensus-ADMM algorithm that respects each subsystem’s local information and communication constraints. We validate our approach on a power network with 36 interconnected subsystems.