An optimal controller architecture for poset-causal systems

Abstract

We propose a novel and natural architecture for decentralized control, that is applicable whenever the underlying system has the structure of a partially ordered set (poset). This controller architecture is based on the Möbius transform of the poset, and enjoys simple and appealing separation properties, since the closed-loop dynamics can be analyzed in terms of decoupled subsystems. The controller structure provides rich and interesting connections between concepts from order theory such as Möbius inversion and control-theoretic concepts such as state prediction, correction, and separability. In addition, using our earlier results on ℌ2-optimal decentralized control for arbitrary posets, we prove that the ℌ2-optimal controller in fact possesses the proposed structure, thereby establishing the optimality of the new controller architecture.