Learning from Demonstration offers great potential for robots to learn to perform agricultural tasks, specifically selective harvesting. One of the challenges is that the target fruit can be oscillating while approaching. Grasping oscillating targets has two requirements: 1) close tracking of the target during the final approach for damage-free grasping, and 2) the complete path should be as short as possible for improved efficiency. We propose a new method called DualLQR. In this method, we use a finite horizon Linear Quadratic Regulator (LQR) on a moving target, without the need of refitting the LQR. To make this possible, we use a dual LQR set-up, with an LQR running in two separate reference frames. Through extensive simulation testing, it was found that the state-of-art method barely meets the required final accuracy without oscillations and drops below the required accuracy with an oscillating target. DualLQR, on the other hand, was found to be able to meet the required final accuracy even with high oscillations, while travelling the least distance. Further testing on a real-world apple grasping task showed that DualLQR was able to successfully grasp oscillating apples, with a success rate of 99%.