A control law for a nonlinear heat conduction problem on nontrivial domains using FEM

A modeling and control strategy is presented for a nonlinear problem of heating a domain of nontrivial geometry from an arbitrary initial to another arbitrary desired temperature profile. A large dynamic model of the nonlinear heat equation is obtained through finite element (FE), which is reduced using proper orthogonal decomposition. Finally, a nonlinear control law is proposed for the control problem and its stability proved through Lyapunov analysis. Results of numerical implementation are presented and possible extensions identified.