Method for closed-loop controlling or controlling linear or non-linear dynamic systems of a heat pump system with a left-turning thermodynamic Clausius-Rankine cycle process, the heat pump system having - at least one closed-loop-controlled electrically driven refrigeration compressor for working fluid, - at least one closed-loop-controlled expansion valve for working fluid, - at least two heat exchangers (3, 5) for working fluid, through which heat transfer fluids flow, - a connection to a heating circuit with a forward flow and a return flow for one of the heat transfer fluids, - at least two electrically driven and closed-loop-controlled conveying devices for the exchange fluids - measuring points for state variables for working fluids and heat transfer fluids, - a device for electronic closed-loop controlling, characterised in that - all operating limits for pressure, temperature, rotary speed and valve openings are incorporated into the closed-loop controlling as limit variables, - a model of all significant dynamic properties of the input and output variables is made to serve as a basis for the closed loop controlling, with which model, for each closed-loop controlling intervention, an estimation of the output variables after this closed-loop controlling intervention is carried out - these estimated output variables of the system are incorporated into the closed-loop controlling and a predictive horizon is determined, - the control variables of all actuators are calculated therefrom, - the controlling of all control variables is carried out simultaneously, - the target temperature of the heat transfer fluid for the forward flow of the heating circuit of the heat pump system is selected as a first guiding variable for the remaining control variables, - the electrical total energy consumption of the entire heat pump is measured and recorded, - as a second guiding variable, the COP value is selected, wherein a predetermined target temperature of the heat transfer fluid for the forward flow of the heating circuit of the heat pump system is varied, and the COP value is formed from the quotient of the heat output to the heat transfer fluid of the heating circuit and the sum of all electrical consumers of the heat pump system. - at least one closed-loop-controlled electrically driven refrigeration compressor for working fluid, - at least one closed-loop-controlled expansion valve for working fluid, - at least two heat exchangers (3, 5) for working fluid, through which heat transfer fluids flow, - a connection to a heating circuit with a forward flow and a return flow for one of the heat transfer fluids, - at least two electrically driven and closed-loop-controlled conveying devices for the exchange fluids - measuring points for state variables for working fluids and heat transfer fluids, - a device for electronic closed-loop controlling, - all operating limits for pressure, temperature, rotary speed and valve openings are incorporated into the closed-loop controlling as limit variables, - a model of all significant dynamic properties of the input and output variables is made to serve as a basis for the closed loop controlling, with which model, for each closed-loop controlling intervention, an estimation of the output variables after this closed-loop controlling intervention is carried out - these estimated output variables of the system are incorporated into the closed-loop controlling and a predictive horizon is determined, - the control variables of all actuators are calculated therefrom, - the controlling of all control variables is carried out simultaneously, - the target temperature of the heat transfer fluid for the forward flow of the heating circuit of the heat pump system is selected as a first guiding variable for the remaining control variables, - the electrical total energy consumption of the entire heat pump is measured and recorded, - as a second guiding variable, the COP value is selected, wherein a predetermined target temperature of the heat transfer fluid for the forward flow of the heating circuit of the heat pump system is varied, and the COP value is formed from the quotient of the heat output to the heat transfer fluid of the heating circuit and the sum of all electrical consumers of the heat pump system.