Homogenization in reaction-diffusion PDEs under space and time-dependent heterogeneities

We study spatial homogenization of nonlinear reaction-diffusion PDEs subject to a class of spatially and temporally-varying heterogeneities. We show that an incremental passivity property in the nominal reaction dynamics is fundamental in guaranteeing homogenization of trajectories. Our distributed control achieves homogenization by defining an internal model subsystem for each output corresponding to the respective heterogeneity. We illustrate our algorithm on a system with bistable dynamics. The main contribution of the paper is a constructive approach to guarantee spatial homogenization under heterogeneities.