Control under structural constraints: An input-output approach

In this paper 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 l(1) H-infinity and H-2 optimal control problems under the so-called onestep 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, l(1), H-infinity and H-2 optimization transform to nonstandard, yet convex problems. Their solution can be obtained by suitably utilizing the Duality, Nehari and Projection theorems respectively.