A Synthesis Approach for Distributed H2 Control Problems with Communication Delays

Yuanji Zou, Nicola Elia

Abstract: In this paper, we find the solution to the discrete-time optimal $H_{2}$ control problem distributed over networks with arbitrary graphs that include communication delays. We assume that the controller is interconnected by a communication topology identical to the physical topology of the networked plant. Our configuration satisfies the quadratic invariance condition. We follow the Youla parameterization framework for the distributed control synthesis setup. We show that the optimal solution is finite-dimensional and can be computed explicitly by solving three algebraic Riccati equations and a Riccati backward recursion. Two of the DAREs are standard for centralized $H_{2}$ control, while the third arises from the sparsity constraints. The backward recursion determines the optimal actions needed to handle the delays. Finally, we validate this methodology on a 4-car platoon system and compare it to the optimal centralized controller, the optimal delay-free structured controller, and a decentralized PID controller.