Distributed Design Methods for Linear Quadratic Control and Their Limitations

We introduce the notion of distributed design methods, which construct controllers by accessing a plant´s description in a constrained manner. We propose performance and information metrics for these design methods, and investigate the connection between closed-loop performance of the best controller they can produce and the amount of exchanged information about the plant. For a class of linear discrete-time, time invariant plants, we show that any communication-less distributed control method results in controllers whose performance is, at least, twice the optimal in the worst-case. We then give a bound on the minimal amount of exchanged information necessary to beat the best communication-less design strategy. We also show that, in the case of continuous-time plants, the worst-case performance of controllers constructed by communication-less design strategies is unbounded.