An Optimal Controller Architecture for Poset-Causal Systems

Details An Optimal Controller Architecture for Poset-Causal Systems An Optimal Controller Architecture for Poset-Causal Systems

2011-11-30

arxiv.org/abs/1111.7221v1

Mathematics

Optimization and Control

32 pages, 9 figures, submitted to IEEE Transactions on Automatic Control

Scientific paper

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 concept of Moebius inversion for posets, 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 Moebius inversion and control-theoretic concepts such as state prediction, correction, and separability. In addition, using our earlier results on H_2-optimal decentralized control for arbitrary posets, we prove that the H_2-optimal controller in fact possesses the proposed structure, thereby establishing the optimality of the new controller architecture.

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