Multi-agent system modeling of advection-diffusion-reaction equations

This work addresses a problem of model-order reduction for a wide class of Partial Differential Equations (PDE). Starting from the popular continuity equation, describing a general conservation law in space, a typical advection-diffusion-reaction equation is illustrated and then turned into a finite-dimensional system by means of reasonable approximations of the processes involved. The reduced-order model takes the form of a Linear Time-Varying (LTV) system, inheriting qualitative and quantitative properties of the original infinite-dimensional model. Convergence properties are discussed and illustrated, also highlighting connections with known results on multi-agent systems. Preliminary numerical simulations show the effectiveness of the proposed approach.