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An algorithm for applying advanced control concepts in heating, ventilating, and air-conditioning systems has been developed at the Los Alamos Scientific Laboratory. The algorithm uses optimal control and is adaptive in nature. Simulations for a solar heated and cooled building indicate that use of this algorithm has the potential of accomplishing a substantial savings in auxiliary energy consumption. In this paper, the algorithm is described and its application is illustrated with a simple example. Simulation results for a more complex system are also presented. The role of the algorithm as a direct digital controller is described, and the hardware, including the digital computer, needed to implement this algorithm is briefly discussed.