# Real-Time Model Predictive Control of Human Bodyweight Based on Energy Intake
## 1 Introduction  
Managing one's own weight can be a difficult task to perform [1]. In order to assist people in managing their weight, it is important to know the required calorie intake. An imbalance in energy intake versus energy expenditure over a longer period can lead to severe changes in body weight [2]. A positive energy balance, meaning that the energy intake is higher than the energy expenditure, results in an increase in body fat [3]. A long-term positive energy balance can lead to overweight (body mass index (BMI) = 25-29.9 kg\(\cdot\)m\({}^{-2}\)) or even obesity (BMI \(\geq\) 30 kg\(\cdot\)m\({}^{-2}\)), a syndrome that negatively affects the cardiovascular system [4]. Obesity is associated with different clinical manifestations such as diastolic dysfunction [5], cancers [6], atrial fibrillation due to pericardial fat [7], hypertension and coronary heart diseases [4]. In 2010, obesity caused more than 3 million deaths worldwide [8]. In 1975,the total number of obese men and women amounted up to 34 million and 71 million, respectively. These numbers rose up to 266 million men and 375 million women in 2014 [4], reaching more than 1.9 billion overweight people in 2016 [9]. Furthermore, the most worrisome trend is the rising rates of obesity in children and adolescents, the prevalence of which tripled between 1971 and 2002 [10]. By contrast, a negative energy balance leads to being underweight. Its prevalence in developed nations is increasing due to voluntary and involuntary caloric restriction [3]. Therefore, a prolonged imbalance in energy intake is a risk factor for several diseases (e.g., diabetes, anorexia of ageing) and affects a large number of people. Thus, it is important to find new and more efficient ways to monitor and control body weight [11]. Health professionals (e.g., dietitians, physical trainers) are qualified to assist individuals in their quest to obtain an optimized energy balance. Based on our own research, we have proven that digital applications (e.g., use of smartphone, wearables... ) can assist in optimizing the energy balance and the health professionals are considered as buddies [12]. Nowadays, smartphones and wearables are suitable tools to collect and process information. The built-in digital cameras, sensors, storage capabilities and wireless connectivity of smartphones can be beneficial for automatic dietary monitoring [13; 14]. In addition, smartphone applications are able to give direct feedback and are already used as tools to monitor physical health [15]. Currently, there are numerous smartphone applications available to track in an individualized and objective manner weight, physical activity and dietary energy intake [16; 17]. However, studies show that the engagement of individuals with these apps decreases after some time, even when personalized suggestions are provided [18; 19; 15]. One of the contributing aspects to this may rely on the fact that nowadays, empirical equations describing the nutrition process are used to predict weight loss and/or to advise dietary energy intake levels. Although these equations are extremely relevant to gather knowledge about the nutrition process, their parameters are estimated at a population-based level. Therefore, inaccurate predictions or suggestions are obtained when applied to data from a single individual. This can diminish the trust in the smartphone app, leading to a loss of engagement and adherence to the suggestions, finally quitting its use [18; 19; 20]. Past and current theoretical models describing the nutrition process are based on the first thermodynamics law on energy conservation [2; 21]. Based on some of the earliest models proposed, still nowadays, many health institutions recommend reducing daily calorie intake with 2 MJ to lose 0.5 kg in 1 week, known as the 3500 kcal rule [21]. However, comparisons between weight loss predicted by the 3500 kcal rule and dynamic models are performed, confirming the invalidity of this rule [22; 23].