2004.03.05.09 edited Decentralized Control Subject to Communication and Propagation Delays

In this paper, we prove that a wide class of distributed control problems subject to communication and prop-agation delays are equivalent to convex optimization problems. The results hold in both continuous and dis-crete time, for both stable and unstable systems. A speci¯c example is formation °ight, where each aircraft has its own controller, and the e®ects of an aircraft's control actions propagate to neighboring aircraft with a delay inversely proportional to the speed of sound. Here each controller may transmit sensor measurements from its aircraft to neighboring aircraft with an associ-ated communication delay, and a consequence of these results is that if the communication delay is less than this propagation delay, then norm-optimal controllers may be found via convex programming.