Systems & control letters / On the use of state constraints in optimal control of singular PDEs ; Syst. & Control Lett. (Netherlands) / On the use of state constraints in optimal control of singular PDEs ; Systems and control letters / On the use of state constraints in optimal control of singular PDEs

We consider optimal control of nonlinear partial differential equations involving potentially singular solution-dependent terms. Singularity can be prevented by either restricting controls to a closed admissible set for which well-posedness of the equation can be guaranteed, or by explicitly enforcing pointwise bounds on the state. By means of an elliptic model problem, we contrast the requirements for deriving the existence of solutions and first order optimality conditions for both the control-constrained and the state-constrained formulation. Our analysis as well as numerical tests illustra... Mehr ...