Boundary Geometric Control of Nonlinear Diffusion Systems

The paper addresses the boundary control of a nonlinear diffusion system submitted to Neumann actuation. The control law is designed in the framework of geometric control theory using directly the nonlinear partial differential equation model without any previous reduction. First, an equivalent linear model using the Cole-Hopf transformation is obtained, then the manipulated variable is inserted in the state equation of this equivalent linear model by means of a Dirac delta function to make the boundary condition homogeneous. Based on the resulting final model, the control law is derived using the characteristic index notion and the closed loop stability is demonstrated using concepts from the powerful semigroup theory. The control law performance is evaluated through numerical simulation by considering a nonlinear heat conduction control problem.