Estimation via Mobile Sensors for Semilinear Time-Fractional Diffusion Processes

The purpose of this letter is to solve an extended observer design problem for state estimation of the anomalous sub-diffusion processes modeled by the 1D semilinear time-fractional diffusion systems. Toward this aim we introduce the mobile zone sensors, which are guided within a limited spatial support but can move throughout the spatial domain hence improving the estimation performance. An extended Luenberger-type observer that contains a state estimator and the guidance of mobile sensors is then designed to meet the desired design requirements. Finally, we finish with a numerical example to illustrate the effectiveness of our proposed method.