# Real-Time Model Predictive Control of Human Bodyweight Based on Energy Intake
## 3 Results and Discussion
### Simulation Model Predictive Control
Figure 6: Energy intake curves suggested by the MPC system based on the time-invariant parameters TF model when uncertainty is added to the a-parameter estimation (**a**) or in b-parameter estimation (**c**) and the obtained bodyweight curves when following these respective energy curves (**b**) and (**d**), after 100 Monte Carlo simulations are performed. represents the energy intake efficiency; thus, slight changes in this parameter induce changes in the energy required to achieve a target bodyweight. However, uncertainty in the _a_-parameter should be limited as well, because an increase in uncertainty may lead to an unstable model. Therefore, these results point out again towards the need to use time-variant parameters models, such the DARX model tested in this study, to obtain accurate estimations of the model parameters and their time evolution for individual participants. Accounting in the model parameters for this variability improves considerably the capabilities of the MPC to suggest energy intake levels which take the individuals variability into account, enabling it to get the closest possible to the targeted bodyweight. In [41], the growth trajectory of broiler chickens is controlled based on an adaptive dynamic model. Here, the performance of the MPC algorithm is quantified by calculating the mean relative error (MRE) between the actual and target weight trajectory of the broiler chickens. The MRE values ranged between 3.7% and 7.0%. For broiler chickens, it is important that the actual growth trajectory resembles the target trajectory, in order to suppress negative effects associated with fast growing broiler chickens. Examples of negative effects include decreased reproduction capacity of the breeder stock, increased body fat deposition and metabolic diseases, such as sudden death syndrome [41]. In [43], the MPC developed in [41] was tested in commercial broiler settings. In this case, the MRE ranged between 6% and 11% under these conditions. Translating the NRMSE and RMSE results from this work to MRE values, obtains, on average, a MRE of \(0.65\pm 0.07\%\) and \(0.34\pm 0.06\%\) when comparing the experimental measured bodyweight curve for each participant and the bodyweight curve obtained following the suggestions from the MPC using time-invariant parameters and time-variant parameters models, respectively. Moreover, MRE of \(0.12\pm 0.01\%\), \(0.18\pm 0.02\%\) and \(0.15\pm 0.03\%\) are obtained when comparing the theoretical bodyweight reference trajectory curves and those obtained when following the MPC suggestions for the theoretical reference trajectories 1, 2 and 3, respectively. Therefore, the MPC's developed in this work show that they are capable of following different bodyweight reference trajectories accurately. Similarly as in the case of the time-variant parameters models, the MPC's developed in this work exhibit a high accuracy when compared with the ones developed for livestock applications. Thus, this enables dietitians to develop a theoretical bodyweight curve and test the energy intake suggested to fulfill this goal in an individualized manner for their patients. Besides, taking advantage of the adaptive capabilities of the MPC, it is possible to modify in real-time this bodyweight reference trajectory according to the performance of the patient and health considerations. In [11; 34], dynamic models are developed to control bodyweight dynamics. These models are dynamic in the sense of accounting for the time evolution of the bodyweight and energy processes. However, these models do not account for the time evolution of the model parameters or the individualized estimation of those parameters working in real-time. These dynamic models still rely on average mechanistic descriptions of the bodyweight and energy flux dynamics. Thus, these approaches lack the adaptability characteristics of the MPC developed in this work. However, a MPC as developed in this work has still some drawbacks to be taken into account in the future.