Communication complexity in the distributed design of linear quadratic optimal controllers

We consider a control design situation in which the knowledge of a linear time-invariant (LTI) plant¿s model is segmented between two parties: one party knows the dynamics of a subsystem within the plant, and how some particular inputs affect the whole system, while the other party knows all the remaining information. We ask: ¿how much of their partial knowledge of the model should the parties transmit to the control designer in order to enable her to construct an optimal controller?¿ Assuming that models are specified by their state-space representations, we tackle this question within the framework of Real Number Communication Complexity theory and prove that, for certain patterns of segmented model knowledge, the communication complexity of optimal control design is maximal. We also show that satisfactory suboptimal controllers can be constructed with reduced communication complexity.