## 4 Simulation Results
### Case (1): Holographic Optical Tweezers Manipulate Control for Single Cells  
The size of the yeast is set as 6 \(\upmu\)m, the initial position is [15; 1; 1; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 98; 99; 100; 101; 102; 103; 104; 105; 106; 107; 108; 109; 110; 111; 111; 112; 113; 114; 115; 116; 117; 118; 119; 120; 121; 122; 123; 124; 125; 126; 127; 128; 129; 130; 131; 132; 133; 134; 135; 136; 137; 138; 139; 140; 141; 142; 143; 144; 145; 146; 147; 148; 149; 150; 151; 152; 153; 154; 155], It can be seen from Table 1 that when the viscous resistance coefficient \(\delta/k\) of the liquid environment is taken as 0.09, and the maximum moving speed is 10 \(\upmu\)m/s 40. Because the cells are controlled by the optical trap, which is generated by the holographic optical tweezers system, the maximum moving speed of the output optical trap is also 10 \(\upmu\)m/s, and the maximum moving distance of the optical trap is less than \(r_{0}\). In practical applications, there are often some obstacle cells and other obstacles in the environment where biological cells are located. A trajectory \(\boldsymbol{q}^{d}\) which satisfies the cells to reach the expected position without collision can be set in advance, such as the expected cell trajectory containing trigonometric functions [38; 40], so that the biological cells can smoothly reach the expected position along the preset trajectory [12; 42]. The expected trajectory \(\boldsymbol{q}^{d1}=\left[{q_{x}}^{d1},{q_  
effectively reach the desired position at the initial time. Because the maximum moving distance of the optical trap is limited, the trajectory error can also be minimized. Considering the sensitivity of micromanipulation to environmental interference, the interference term \(d=\left[d_{x},d_{y}\right]^{T}\) is set, where \(d_{x}\) and \(d_{y}\) are the interference terms in the \(X\)-axis direction and the \(Y\)-axis direction, respectively. \[ \begin{cases}d_{x}=0.5\sin(0.05t),\quad 0\text{ s}\leq t\leq 5\text{ s}\\ d_{y}=0.3\cos(0.03t),\quad 0\text{ s}\leq t\leq 5\text{ s}\end{cases}  \tag{61}\]  
In the simulation experiment in this section, the sampling time is set to 0.1 s, the simulation time \(t_{max}=60\) s, and the trajectory constraint parameter \(r_{x}=r_{y}=3\). In order to verify the control performance of the NSOFCMNN controller, the PI controller, BP neural network controller and FCMNN controller are also used for comparison with the NSOFCMNN in this paper. The number of iterations of each neural network is set to 50, and the sliding surface parameter \(\mathbf{K}=[0.3x_{1},0.3x_{2}]^{T}\). In the PI controller, \(k_{p}=20\), \(k_{i}=0.5\). The number of hidden layer nodes of the BP neural network is 3, the number of neurons of the RBF neural network is 3, the number of layers of the FCMNN is fixed to 3, and the number of blocks is fixed to 3. The initial number of layers and initial blocks of the NSOFCMNN are both 3, and the self-organizing structure adjustment parameter \(T_{n}=0.01,\ T_{m}=0.0001,\ T_{k}=0.32\). Figure 5 shows the comparison between the expected trajectory without constraints and the trajectory of a single cell manipulated by the optical trap which is generated by the holographic optical tweezers system when using NSOFCMNN as the main controller. Due to the addition of the trajectory constraint parameters \(r_{x}\) and \(r_{y}\), the controlled yeast cells will not be immediately moved to the unconstrained expected trajectory at the initial time, but will move along the constrained expected trajectory in Equations (59) and (60). It is ensured that the trajectory error is not affected by the maximum moving distance \(r_{0}\) of the optical trap.