Contents I. Introduction
An important research area that has received a lot of attention in recent years is control design for spatially distributed systems (SDSs), mathematically modeled by partial differential equations (PDEs). The key characteristic of SDSs is that their outputs, inputs, states, and relevant parameters may vary temporally as well as spatially. Due to their infinite-dimensional nature, the theory of SDSs (see [1]–[4]) has focused on the methods (-semigroups, operator equations, etc.) for the precise mathematical treatment of these SDSs, which is significantly more difficult than the finite-dimensional theory. The constructive aspects of these theories typically deal with ensuring that the finite-dimensional approximation schemes converge. Problems with spatially distributed sensing and actuation pose an additional challenge, in that finite-dimensional approximations always produce systems with large-scale inputs and outputs. With few exceptions, such problems have not been thoroughly studied due to the perception of their technological infeasibility.
