Optimal control of systems with delayed observation sharing patterns via input-output methods

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, we consider norm minimization optimal control problems under the so-called one-step delay observation sharing pattern. We present a Youla parametrization approach that leads to their solution by converting them to nonstandard, yet convex, model matching problems. This conversion is always possible whenever the part of the plant that relates controls to measurements possesses the same structure in its feedthrough term with the one imposed by the observation pattern on the feedthrough term of the controller, i.e., (block-)diagonal. When that is not the case, it amounts to the so-called non-classical information pattern problems. For the ℋ^∞ case, using loop-shifting ideas, a simple sufficient condition is given under which the problem can be still converted to a convex, model matching problem. We also demonstrate that there are several nontrivial classes of problems satisfying this condition. Finally, we extend these ideas to the case of a N-step delay observation sharing pattern.