On optimal thermal control of an idealized room including hard limits on zone-temperature and a max-control cost term

We study an open-loop optimal control problem for energy efficient cooling of a simple room. The goal is to provide insights for the development of an implementable control scheme based on a Model Predictive Control strategy. The cost function includes a non-standard Mayer-term F(max_t u(t)); that is, a term depending on the peak value of the control. Comfort requirements are imposed as state inequality constraints.