Localized Distributed Optimal Control with Output Feedback and Communication Delays

This paper presents an output feedback control scheme for localizable distributed systems subject to delay, that is to say systems for which the effect of both process noise and sensor noise can be localized in closed loop despite communications delays between controllers. By reformulating the distributed optimal control problem in terms of the closed loop transfer matrices from sensor and process noise to controlled output, we cast the optimal localized distributed control problem as a finite dimensional affinely constrained convex program. We additionally show how to synthesize the controller achieving the desired closed loop response, and that the controller can be implemented in a localized and thus scalable manner, which is essential when applying the scheme to large scale systems. Simulation shows that for certain systems, our optimal controller, with its constraints on locality, settling time, and communication delay, can achieve similar performance to a centralized optimal one.