This work focuses on distributed control of diffusion - reaction processes described by quasi-linear parabolic partial differential equations (PDEs) and addresses the problem of enforcing a prespecified spatio-temporal behavior in the closed-loop system using nonlinear feedback control and a large number of sensors and actuators. Under the assumption that the desired spatio-temporal behavior is described by a "target parabolic PDE", we use combination of Galerkin's method and nonlinear control techniques to design nonlinear state and static output feedback controllers to address this problem. We use an example of a diffusion-reaction process to demonstrate the formulation of the control problem and the effectiveness of our systematic approach to creating prespecified spatio-temporal behavior. Using this illustrative example, we demonstrate that both (a) large number of actuators/sensors, and (b) nonlinear control laws are necessary to achieve this goal.
All Science Journal Classification (ASJC) codes
- Electrical and Electronic Engineering