Control of Reaction-Diffusion Processes Under Communication Delays

In this paper we investigate the design of optimal spatially distributed controllers for a linear and spatially invariant reaction-diffusion process over the real line. The controller receives state measurements from different spatial locations with non-negligible delays. In this set-up and for the class of proportional spatially invariant state feedback controllers, the optimal control synthesis problem is equivalent to a feedback gain optimization for a spatially distributed delay system. We show that the spatial locality of optimal feedback gains is affected not only by diffusion and reaction coefficients, but also by the parameter representing communication time-delay that causes a sharp flattening of the control gains. In the expensive control regime, the optimal controller is solved analytically, yielding some practical design guidelines.