Optimal Distributed Controllers Realizable over Arbitrary Networks

In this paper, we provide a general networked controller design methodology for networked plants and apply it to solve the optimal H₂ networked control problem. Both the plant and the controller are interconnected systems, interacting over the same arbitrary directed network with noiseless and delay-free communication links. We introduce the notions of network implementability and network realizability and analyze the structure of network implementable and realizable systems. Based on the structural property of network implementable systems, under certain network-related constraints, we characterize the set of all stabilizing controllers that are implementable over the given network using the state-space version of Youla parametrization. Moreover, we provide a constructive procedure to implement the controllers as sub-systems interacting over the given network without affecting the stability of the feedback networked system. The distributed H₂ control problem is then cast as a convex optimization problem and its solution is shown to provide the optimal distributed controller over the given network in terms of its network interacting components. The results of this paper allow one to apply many classical results and approaches of multi-variable robust control theory to networked systems.