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The recent significant expansion of electric space heating calls for proper load management strategies for a northern climate. In this paper, a multimode system including heat pump technology with storage is developed. The variations of the room temperature setpoint are studied in relation to heating power and the setback pattern. A discrete-time solution to the problem of determining the optimal amount of energy required from an electrical source in order to minimize consumption and temperature droop has been obtained. The present solution is suboptimal in the sense that it is a linear approximation of a non-linear plant. The recursive Kalman filter was employed for the linear regulator solution. Pontryagin's minimum principle was used to express the singular algorithm. The implementation problems of the above feedback controllers are discussed. Numerical results from computer simulations are compared with the bang-bang regulator performances. A real-time adaptive control application using hourly predictions of climatic conditions is foreseen.