Optimal sensor placement for state reconstruction of distributed process systems

In this contribution we propose a systematic approach to field reconstruction of distributed process systems from a limited and usually reduced number of measurements. The method exploits the time scale separation property of dissipative processes and concepts derived from principal angles between subspaces, to optimally placing a given number of sensors in the spatial domain. Basic ingredients of the approach include the identification of a low-dimensional subspace capturing most of the relevant dynamic features of the distributed system, and the solution of a max-min optimization problem through a guided search technique. The low-dimensional subspace can be defined either through a spectral basis (eigenfunctions of a linear or linearized part of the operator) or through a semiempirical expansion known in the engineering literature as the Proper Orthogonal Decomposition (POD) or Karhunen-Loeve expansion. For both cases, the optimal sensor placement problem will be solved by taking advantage of the underlying algebraic structure of the low-dimensional subspace. The implications of this approach for dynamic observer design will be discussed together with examples illustrating the proposed methodology.