Yuexin Cao: Network Controllability and Spectrum Optimization of Turing's Reaction-Diffusion models

In this talk, we will introduce Turing's reaction-diffusion model from the perspective of systems theory. Turing's model was the first model proposed to explain the self-organizing process in organisms and now is widely used in the field of information theory. We will discuss two fundamental questions about the control placement strategy: How to place the controls to drive the Turing's model to our desired states, i.e., system controllability, and if it is controllable, how to place the controls to optimize the energy cost. Specifically, we will first introduce the minimal number of controls for the controllability and provide a general policy for the control placement problem. Then we provide a method to compute the eigenvalues and eigenvectors of the controllability Gramian more efficiently and present an algorithm for the spectrum optimization.