Using process tomography as a sensor for optimal control

In this paper, model-based control is discussed when the observations are based on diffuse tomography such as impedance tomography. Diffuse tomography is a notoriously difficult class of inverse ill-posed problems which in the case of control system design means that the computation of the state estimates is basically an unstable problem. Recent results in the field of nonstationary inverse problems have shown that accurate modeling of the state and observation models may facilitate stable state estimation, which in turn would facilitate feedback control. When the state evolution model is based on partial differential equations, the price to pay is that the dimension of the state is invariably very large since state reduction leads to intolerable approximation errors. In this paper, the basic LQG control design based on impedance tomographic measurements is considered when the state is governed by a stochastic convection-diffusion equation. It is shown with simulations that proper stochastic modeling of the state evolution can enable one to obtain such state estimates that facilitate feedback control.