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Air-to-water heat pumps are one of the most common and energy efficient heating systems for buildings, particularly floor-heating plants. One way to further improve their effectiveness is to control the heat pump exploiting the dependence of its coefficient of performance (COP) on the external temperature and temperature of the return water from the load. In particular, it is possible to exploit the heat pump when its efficiency is higher, so optimizing its performance in a predictive manner, anticipating the impact of external conditions. For the case of an air-to-water heat pump, the optimization problem is nonlinear due to the load dependence of the heat pump COP and variable supply water flow rate. This may pose implementation problems. If we address a standard control hardware, simplified optimal control formulations are more effective. In this paper, we specifically address this issue, and a reduced-order, linear, but adaptive time-varying predictive model of the heat pump COP is designed. Our solution takes into account the variation of the heat pump efficiency based on the external temperature and the load profile, which are changing within the control horizon. The proposed COP model is then used within a linear time-varying model predictive controller formulation which provides a prediction of the heat pump dynamical behavior based on the load dependence of the heat pump COP, while tackling the nonlinearities of the system imposed by the variable water flow rate in the hot water tank and also by the load dependence of the heat pump COP. The proposed approach has been implemented and in detail tested on a reference model based on a real case study from the Denmark Technical University, Risø Campus, SYSLAB. An intensive simulation analysis and complements the testing, showing the accuracy and the potential of the method, also in the perspective of practical implementation. • Optimization of heat pump behavior considering variable COP. • On-line estimation of simplified COP models with EKF. • Experimental validation of the model used. • Feasibility of realtime optimization proved. [ABSTRACT FROM AUTHOR]