A heuristic for sub-optimal ℌ2 decentralized control subject to delay in non-quadratically-invariant systems

Inspired by potential applications to the smart grid, we develop a heuristic for sub-optimal, but acceptable, control of decentralized systems subject to non-quadratically invariant (non-QI) delay patterns. We do so by exploiting a recently developed solution to the decentralized H₂ model matching problem subject to delays, which decomposes the controller into a centralized, but delayed, component and a decentralized FIR component. In particular, we present an iterative procedure that exploits this decomposition to design a sub-optimal decentralized H₂ controller for non-QI systems that is guaranteed a priori to be stable, and to perform no worse than a controller computed with respect to a QI subset of the non-QI constraint set. We then apply this procedure to a smart-grid frequency regulation problem.