Optimal control of systems with delayed observation sharing patterns

We present an input-output point of view of certain optimal control problems with constraints on the processing of the measurement data. In particular, considering linear controllers and plant dynamics, we present solutions to the l¹, ℋ^∞ and ℋ² optimal control problems under the so-called one-step delay observation sharing pattern. Extensions to other decentralized structures are also possible under certain conditions on the plant. The main message from this unified input-output approach is that, structural constraints on the controller appear as linear constraints of the same type on the Youla parameter that parametrizes all controllers, as long as the part of the plant that relates controls to measurements possesses the same off diagonal structure required in the controller. Under this condition, l¹, ℋ^∞ and ℋ² optimization transform to nonstandard, yet convex problems. Their solution can be obtained by suitably utilizing the duality, Nehari and projection theorems respectively