## 3 Results and Discussion  
In this section, we present the results obtained from validating the performance of the proposed method in this research. Figure 6 illustrates the characterization of the parameter space \((\Delta,\left|S\right|^{2})\) for rings with an FSR of 200 GHz and 50 GHz. Note that the lower-right portion (SCS) shows the region with optical combs that exhibit a larger number of spectral lines (DKS), and we identify it in magenta. We propose a non-linear path design in [42] to avoid the chaotic region and enable reliable comb generation due to the difficulty of generating this comb type. Figure 8a,e show the proposed paths in black. It is important to note that the MRR in Figure 8a facilitates DKS generation by possessing a zone with higher amplitude. In contrast, the MRR in Figure 8d demonstrates the less frequent appearance of these states, indicating that their generation poses a difficulty for this geometry. To estimate the functions that describe the dynamics of the proposed paths, we utilize the curve-fitting tool and estimate models of Equations (5) and (6) using data from the parameter spaces \((\Delta,\left|S\right|^{2})\). The path proposed for the MRR shown in Figure 8a is defined by Equation (3), while the path for the MRR shown in Figure 8b is defined by Equation (4). \(\Delta\) linearly varies in the range [0, 5.219] and [0, 5.4105] for the 50 GHz and 200 GHz MRR, respectively. \[\left|S\right|^{2}=3\text{exp}(-1.38\Delta)+1.060\text{exp}(0.2795\Delta) \tag{5}\]  
\[\left|S\right|^{2}=3.067\text{exp}(-1.181\Delta)+0.9499\text{exp}(0.30843\Delta) \tag{6}\]  
After calculating the paths, we perform a Monte Carlo experiment to assess the variability in generating these paths for each MRR without the control rule. This experiment randomly varies the initial state of the field by introducing E(w) as a complex Gaussian and verifies the achievement of the DKS. Figure 9 shows the results of the Monte Carlo experiment, where frequency combs ranging from 1 to 5 pulses are obtained over 200 repetitions, regardless of the variation in noise introduced in the simulation (see Figure 9d,h). DKS generation exhibits probabilistic behavior since every simulation does not achieve it. Despite this result, the DKS appears with a probability greater than 50% for the 50 GHz and 200 GHz MRR, respectively. The significance of these results is that the control strategy can quickly generate the state by repeating the generation a finite number of times. Upon characterizing the paths, the control strategy implements the generation process. This process exploits the DKS appearance probability to achieve a state with minimal repetitions. Figure 10c shows that 200 Monte Carlo experiment simulations always yield the DKS state. This outcome is crucial as it ensures deterministic generation, which is the primary goal of this strategy. Figure 10a,c show the repetition frequency of the generation through the control strategy produces the soliton state between 1 and 11 repetitions. This finding is significant because it does not require many repetitions to achieve the desired state, indicating a time range between 3 and 37 us for this generation, which is appropriate for these communication systems. Figure 8: (**a**) Microring resonator structure with an FSR of 200 GHz. (**b**) Parametric space as a function of peak number \((\Delta,\left|S\right|^{2})\) for the MRR with an FSR of 200 GHz. The arrow is the DKS generation path. (**c**) Region characterization according to variation \((\Delta,\left|S\right|^{2})\) for the MRR with an FSR of 200 GHz. (**d**) Microring resonator structure with an FSR of 50 GHz. (**e**) Parametric space as a function of peak number \((\Delta,\left|S\right|^{2})\) for the MRR with an FSR of 50 GHz. The arrow is the DKS generation path. (**f**) Region characterization according to variation \((\Delta,\left|S\right|^{2})\) for the MRR with an FSR of 50 GHz.