## 4 Simulation Results
### Case (2): Holographic Optical Tweezers Manipulate Control for Multiple Cells
Figure 13 shows the trajectory errors of different controllers when the holographic optical tweezers manipulate multiple cells simultaneously. Each subplot contains the manipulation control error of four controlled yeast cells with virtual cells. When using the PI main controller, the four controlled yeast cells have large errors of the \(X\)-axis and \(Y\)-axis, and the error fluctuates greatly. The PI controller cannot be well applied to the multi-cell control in complex environments. When using the BP main controller, the error fluctuation is smaller, but the error is still larger. When using RBF, FCMNN or NSOFCMNN as the main controller, the error is small and can gradually converge. Moreover, the control accuracy of the proposed NSOFCMNN as the main controller far outperforms the other main controllers. Figure 11: Relative distance between the controlled cell and the virtual cell. Figure 12: Comparison between the actual trajectories and the expected trajectories of four controlled cells. Figure 13: Trajectory error using different controllers (multi-cell manipulation). In order to further compare the difference of the control effect of each controller in the multi-cell manipulation, RMSE and MAE are also used as control performance comparison indicators to compare the specific errors between them. According to Formulas (62) and (63), Tables 4 and 5 are obtained. Since the expected trajectory function set in Section 4.2 is more complex than that in Section 4.1, and the controller controls four controlled yeast cells and one virtual cell at the same time, it requires higher network performance. The RMSE and MAE of each controller are shown in Tables 4 and 5, respectively. It can be seen that the RMSE of the manipulation control of PI, BP or RBF as the main controller is in the interval of [1.9 \(\times\) 10\({}^{-6}\), 5.1 \(\times\) 10\({}^{-6}\)], [2.7 \(\times\) 10\({}^{-10}\), 1.2 \(\times\) 10\({}^{-7}\)] and [3.3 \(\times\) 10\({}^{-8}\), 7.7 \(\times\) 10\({}^{-8}\)], respectively. The corresponding MAE is in the interval of [4.0 \(\times\) 10\({}^{-6}\), 3.1 \(\times\) 10\({}^{-5}\)], [4.0 \(\times\) 10\({}^{-8}\), 7.2 \(\times\) 10\({}^{-6}\)] and [7.9 \(\times\) 10\({}^{-9}\), 2.8 \(\times\) 10\({}^{-8}\)], respectively. As the main controller, FCMNN still has better control performance than the first three neural networks. The RMSE and MAE are between [1.9 \(\times\) 10\({}^{-19}\), 12.4 \(\times\) 10\({}^{-10}\)] and [7.9 \(\times\) 10\({}^{-9}\), 2.8 \(\times\) 10\({}^{-8}\)], respectively. The proposed NSOFCMNN as the main controller, as well as its RMSE and MAE, are both smaller than FCMNN due to the addition of self-organizing structure adjustment rules. The minimum RMSE and the minimum MAE of NSOFCMNN are only 1% of that of FCMNN. It can be concluded that the NSOFCMNN main controller has much more powerful control performance in the multi-cell manipulation of holographic optical tweezers, and it enables more precise manipulation of cells to expected positions. Figure 14 shows the changes in the number of layers and blocks of the proposed NSOFCMNN in the multi-cell manipulation experiment of holographic optical tweezers. It can be observed that the input data generated is larger due to the initially controlled yeast cell position being far from the expected position. The network structure is quickly adjusted from the initial layer number of three layers and the initial number of blocks to three blocks to six layers and four blocks to better improve the learning ability of the NSOFCMNN.