Efficient state constraint handling for MPC of the heat equation

This contribution is concerned with model predictive control (MPC) of systems governed by partial differential equations (PDEs) and subject to state and input constraints. In particular, the numerically efficient handling of the underlying optimal control problem (OCP) is considered. It is shown that the state- and input-constrained OCP can be transformed by using saturation functions into an unconstrained OCP. This then can be solved numerically by means of well-established optimization methods. For a numerically efficient implementation of the MPC, a first discretize then optimize-approach is used in conjunction with a tailored gradient method. Both the transformation into an unconstrained OCP and its numerical solution are investigated for a simple heat conduction problem.