Some solutions for nonlinear optimal heat transfer problems

A short review of some heat transfer optimal control problems arising in building management for energy conservation is given. These problems are non-linear since both the internal energy source and the time-dependent parameters of the building envelope are control variables. In the singular case, optimal control is shown to be bang-bang and in the non-singular case, the equations of the feedback law are derived. Satisfactory numerical simulations are given that illustrate the two approaches of this practical control problem.