We want to control our body weight (system output) by altering how much we eat (system input), based on measurements of our weight, so that it follows a particular trajectory. We could simply try to calculate how much we should eat ahead of time based on this trajectory and our initial weight, and then follow this schedule without updating it based on any subsequent measurements ("open loop control"). However, this would require a very good mathematical model that can accurately predict future weight based on current weight and food intake. If we instead choose how much to eat based on continuous measurements of our weight (using feedback to achieve "closed loop control"), we can get away with using a much worse model; this is one of the key advantages of feedback.

The proposed control algorithm is simple: when eating a meal, eat a total weight of food and drink (F(t)) that is the weight you would like to be at the end of the meal (r(t+T)), minus your weight at the start of the meal (w(t)). This rule ignores metabolism, so you will fall below your target weight by the next meal, but you will eat accordingly more then.

Obviously, as the article notes, this requires that "the reference r(⋅) has to be chosen larger than w(⋅) at all times". You can see this in Figure 1: the measured mass starts below the reference, then increases up to the reference, then falls below it, then increases up to it at the end of each meal.