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Optimizing a heat pump driven forced-air domestic heating system utilizing solar/thermal energy storage and off-peak storage from the electric power network is discussed. The system proposed is modeled and simulated on the digital computer. An optimal controller is then developed to maximize comfort and minimize conventional energy consumption. The controller is then simulated with the heating system for the University of Toledo experimental electric/solar house, Toledo, OH, and shown to be truly optimal and able to control the system in a desirable manner.