Distributed estimation of 1-D convection-diffusion phenomena by discrete-time event-triggered consensus dynamics

This paper considers a consensus-based approach for an inverse problem of the 1-D convection-diffusion equation to estimate an initial distribution of concentration from measurement data. The inverse problem of the convection-diffusion equation can be formulated as a linear least squares problem by a difference approximation. To obtain the solution of the least squares problem in a distributed way, we propose a discrete-time event-triggered consensus dynamics with time-varying communication networks. We show that the least squares problem of the convection-diffusion equation can be solved by the proposed event-triggered consensus dynamics.