An environmental system with two conditioned spaces is considered. Conditioned spaces are assumed to have limited heat transfer through ducts with the ambient, a cold air source and a hot air source as well as with each other. The ducts are equipped with louvers and are idealized by variable thermal resistances. The conditions for optimal control are derived by using Pontryagin’s maximum principle. The control action is shown to be of bang-bang type. A method which makes use of the behavior of the costate variables is used to determine the optimal control sequence. Solutions for a typical physical system show that the time optimal control is achieved by switching the control variables at most two times. The state space is divided into eight regions and within each region one and the same control algorithm applies. The results also show that time optimum control of two capacity thermal systems leads to energy as well as time savings if the two capacities are interconnected by a controllable thermal resistance.

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