Optimal Control of Distributed Arrays with Spatial Invariance

We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of platoons, smart structures, or distributed ow control through the uid boundary. For optimal control problems involving quadratic criteria such as LQR, H2 and H1, it is shown how to reduce the optimization to a family of problems over spatial frequency. We also show that optimal controllers have an inherent degree of decentralization, which leads to a practical distributed architecture. Under a more general class of performance criteria, a general result is given showing that optimal controllers inherit the spatial invariance structure of the plant.