Distributed nonlinear control of diffusion-reaction processes

In this work, we focus on distributed control of quasi-linear parabolic partial differential equations (PDEs) and address the problem of enforcing a prespecified spatio-temporal behaviour in the closed-loop system using nonlinear feedback control and a sufficiently large number of actuators and sensors. Under the assumption that the desired spatio-temporal behaviour is described by a 'target parabolic PDE', we use a combination of Galerkin's method and nonlinear control techniques to design nonlinear state and static output feedback controllers to address this problem. We use examples of diffusion-reaction processes to demonstrate the formulation of the control problem and the effectiveness of our systematic approach to creating prespecified spatio-temporal behaviour. Using these illustrative examples, we demonstrate that both (a) a sufficiently large number of actuators/sensors, and (b) nonlinear control laws are needed to achieve this goal.