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.