Since Newton, scientists have extensively attempted to model the world. In particular, when a mathematical model is available (for instance, Newton's gravitational law or Coulomb's equation for electrostatics), we can foresee, given some parameters that describe a physical system (such as a distribution of mass or a distribution of electric charges), the behavior of the system. This approach is known as mathematical modeling and the above-mentioned physical parameters are called the model parameters or simply the model. To be precise, we introduce the notion of state of the physical system: it is the solution of the mathematical model's equation. In optimal control theory, these equations are referred to as the state equations. In many situations we are not truly interested in knowing the physical state but just its effects on some objects (for instance, the effects the gravitational field has on a specific planet). Hence we have to introduce another operator, called the observation operator, which converts the state of the physical system (here the predicted gravitational field) into what we want to observe (here the movements of the considered planet). We can now introduce the so-called forward problem, which consists of two steps: