Controlled Pattern Formation in a Reaction-Diffusion System: A Novel Application of Non-Linear Model Predictive Control to Distributed Parameters Systems

In this work, we examine the application of open-loop non-linear model predictive control (NMPC) to a specific partial differential equation (PDE) reaction-diffusion system. Instead of attempting to stabilize a particular state, we focus only on reaching the desired state at a given time. This problem is motivated by applications to in-vitro synthesis of tissues whose formation is governed by reaction-diffusion models. The PDE model is discretized into a finite set of nonlinear ordinary differential equations using finite-elements, after which a NMPC algorithm is used to derive the desired control actions. Results for one- and two- dimensional systems demonstrate the feasibility of the approach, but also highlight a dependency on the number of actuators and computational power