# Design of Multi-Cell Cooperative Control Algorithm Based on Fuzzy Brain Emotional Learning
## 3 Single-Cell Manipulation Control
### Cell Manipulation Controller Design  
Changing the trapping force of the cell with holographic optical tweezers is a typical way to alter cell motility. The position of the optical trap center produced by the holographic optical tweezers directly affects the trapping force. Therefore, by altering the center point of each optical trap, the direction of the related cell's movement may be regulated. The holographic optical tweezers can acquire the real-time position of the cell in the altered environment depending on the image processing technology, which is advantageous for better control of the cell. In order to accurately output the position of the optical trap and improve the control accuracy of cell manipulation, a neural network is used as the main controller. The FBEL neural network consists of two systems: the first system is the amygdala, which is similar to the mammalian brain and is involved in emotional judgment. The second system is the orbitofrontal cortex, which controls emotions. This neural network has strong learning ability and fast convergence speed, and can effectively approximate any nonlinear system [30; 31; 32]. The type-lifuzzy logic systems can be used to achieve the fuzzy inference of the proposed FBEL neural network with the center average defuzzifier, product interface rule, singleton fuzzifier, and Gaussian membership function given by IF-THEN fuzzy rules [46]. Considering the two systems of the FBEL neural network model, the fuzzy inference systems of the proposed FBEL neural network also consists of two fuzzy rule bases. One is the amygdala fuzzy system:  
\[\text{If }\text{I}_{1}\text{ is }\text{G}_{1\text{m}}\text{ and }\text{I}_{2}\text{ is }\text{G}_{2\text{m}},\ldots,\text{I}_{\text{N}}\text{ is }\text{G}_{\text{Nm}},\text{ then }\text{A}=D_{\text{nm}} \tag{8}\]  
The other is the orbitofrontal cortex fuzzy system:  
\[\text{If }\text{I}_{1}\text{ is }\text{G}_{1\text{m}}\text{ and }\text{I}_{2}\text{ is }\text{G}_{2\text{m}},\ldots,\text{I}_{\text{N}}\text{ is }\text{G}_{\text{Nm}},\text{ then }\text{O}=B_{\text{nm}} \tag{9}\]  
(for n = 1, 2, \(\ldots\), N, m = 1, 2, \(\ldots\), M), where N is the input dimension, M _represents the number of neurons_. \(G_{nm}\) is the fuzzy set for the \(n\)th input and \(m\)th neuron_, \(D_{mm}\) is the amygdala weight for the output corresponding to the \(n\)th input, and the \(m\)th layer in the consequent space, and A is the output of the amygdala; \(B_{nm}\) is the orbitofrontal cortex weight for the output corresponding to the nth input and the \(m\)th layer in the consequent space, and O is the output of the orbitofrontal cortex. The structure of the FBEL neural network is shown in Figure 3. It can be roughly divided into five layers. The first layer is the input layer. The second layer is the sensory cortex. The third layer is the weight space layer. The fourth layer is the amygdala and orbitofrontal cortex. The fifth layer is the output layer. (1) First layer  
This layer is the data input layer. \[I_{n}\in R^{n},\ \ n=1,2,3,\ldots,\text{N} \tag{10}\] \begin{table}
\begin{tabular}{c c} \hline
**Speed of Cells ( \(\mu\)m/s)** & \(\beta\)/\(k\) \\ \hline \(\pm 5\) & 0.09 \\ \(\pm 7.5\) & 0.1 \\ \(\pm 10\) & 0.09 \\ \hline \end{tabular}
\end{table} 
Table 1: Values of \(\beta\)/\(k\) in yeast cells [45]. (2) Second layer  
Each neuron uses the input signal to activate the sensory cortex for fuzzy reasoning, and the membership function is a Gaussian function with better universality [46; 47]:  
\[G_{nm}=exp\left[\frac{-\left(I_{n}-\varepsilon_{nm}\right)^{2}}{\omega_{nm}^{2}}\right] \tag{11}\]  
where \(m\) represents the \(m\)th neuron, \(\varepsilon_{mn}\) and \(\omega_{nm}\) represent the mean and variance of the Gaussian function, respectively. (3) Third layer  
\(D_{nm}\) holds the weight space of the amygdala and receives the output of fuzzy inference rules from the sensory cortex. \(B_{nm}\) holds the weight space of the orbitofrontal page cortex and also receives the output of fuzzy inference rules from the sensory cortex.