The structure of optimal controllers of spatially-invariant distributed parameter systems

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, flow control with large arrays of sensors/actuators (e.g. in micro electromechanical systems), and systems described by partial differential equations with constant coefficients and distributed controls and measurements. We consider a variety of optimality criteria, and show that optimal controllers inherit the spatial invariance structure of the plant. We comment on the significant implications of this fact to controller design and implementation for such distributed parameter systems.