## 3 Traditional Controllers: PID and MPC Closed-Loop Control Strategies
### Deep Learning Neural Network
#### 4.2.2 NN Table Models  
Neural network tables can take various forms depending on the specific application and the type of data being processed. The most usual NN tables built to analyze NN performance using evaluation metrics include the confusion matrix, the weight matrix, activation tables, and loss tables. In the following, we examine these particular tables.  
1. **Confusion Matrix**: This type of table is used to evaluate the performance of a classification model. It shows the numbers of true positives, true negatives, false positives, and false negatives. A generic example is presented as follows:  
\[\begin{array}{cc}\hline\hline\text{Actual}/\text{Predicted}&\text{Positive}& \text{Negative}\\ \hline\hline\text{Actual}&60&20\\ \hline\hline\text{Predicted}&10&25\\ \hline\end{array}\]
2. **Weight Matrix**: In each NN, the weights are critical parameters that transform input data within the network. A weight matrix represents the weights between layers of neurons, for which a simple matrix might look like this:  
\[\begin{array}{cc}\hline\hline\text{Neuron k}&\text{Neuron k + 1}&\text{Neuron k + 2}\\ \hline\hline\text{0.2}&0.3&-0.1\\ \hline\text{0.3}&0.5&0.2\\ \hline\end{array}\]
3. **Activation Table**: This type of table illustrates the activation values of the neurons in a NN for a given input, as shown below:These tables are essential for analyzing and understanding the performance and behavior of neural networks in various applications. Appendix B.2 details two DLNN tables, namely the Tables A1 and A2 with parameter simulation and monitoring training for the two proposed RL DLNN control algorithms developed in Section 4.3. Since both RL DLNN algorithms solve a tracking reference control regression problem, the most suitable evaluation metrics are RMSE and MSE [17]. The strong dependence of reward function of RMSE and MSE gives us the possibility of using an evaluation metric based on reward function, since the problem of minimization of RMSE or MSE to the smallest possible value closest to zero becomes a maximization problem of reward function, for which the most appropriate metrics are the cumulative reward value (return value) or average reward value. The evaluation metric used for DLNN performance in both NN tables is the average reward value for each training episode, since this value appears automatically in the monitoring of the RL agents' training progress, as shown in Figure 9k,l and Tables A1 and A2 from Appendix B.2. The RL agents are trained using the adopted RL DLNNs control algorithms whose reward functions are generated from MPC and the step response specifications of the MIMO Centrifugal Chiller System discussed below in Section 4.3.  
Reinforcement Learning Deep Learning Neural Networks Closed-Loop Control Strategies Applied to a Centrifugal Chiller System  
In this section, we develop two advanced intelligent reinforcement learning deep learning neural network (RLDLNN) control algorithms to control the evaporator temperature and the level of refrigerant in the condenser. The first algorithm generates a reward function for an RL Agent based on model predictive control (MPC) specifications and the second algorithm generates two reward functions for two RL agents (controllers) based on the step response block specifications.