Why do you say that it is open loop? It is clearly closed loop control.
Note that the voltage on the + pin of U1 is acting as a reference voltage. An increase in the opamp output will drive the transistor base and cause the emitter current to increase. This increase will cause the voltage on the - pin of U1 to increase. If the voltage on the - pin exceeds that of the + pin, then the output of the opamp will be driven down. This lowers the transistor current and lowers the - pin voltage. This is negative feedback. Assuming that the feedback is stable, then the current in the collector and emitter legs of the transistor will be precisely controlled because the + and - pins of the opamp will have nearly equal voltage.