Editing System identification (section)

== Forward model ==

A common understanding in Artificial Intelligence is that the [[Controller (control theory)|controller]] has to generate the next move for a [[robot]]. For example, the robot starts in the maze and then the robot decides to move forward. Model predictive control determines the next action indirectly. The term [[Mathematical model|"model"]] is referencing to a forward model which doesn't provide the correct action but simulates a scenario.<ref>{{cite journal |title=Model learning for robot control: a survey |author=Nguyen-Tuong, Duy and Peters, Jan |journal=Cognitive Processing |volume=12 |number=4 |pages=319–340 |year=2011 |publisher=Springer |doi=10.1007/s10339-011-0404-1|pmid=21487784 |s2cid=8660085 }}</ref> A forward model is equal to a [[physics engine]] used in game programming. The model takes an input and calculates the future state of the system.

The reason why dedicated forward models are constructed is because it allows one to divide the overall control process. The first question is how to predict the future states of the system. That means, to simulate a [[Plant (control theory)|plant]] over a timespan for different input values. And the second task is to search for a [[Sequence of events|sequence]] of input values which brings the plant into a goal state. This is called predictive control.

The forward model is the most important aspect of a [[Model predictive control|MPC-controller]]. It has to be created before the [[solver]] can be realized. If it's unclear what the behavior of a system is, it's not possible to search for meaningful actions. The workflow for creating a forward model is called system identification. The idea is to [[Formal system|formalize a system]] in a set of equations which will behave like the original system.<ref>{{cite journal |title=Learning modular and transferable forward models of the motions of push manipulated objects |author=Kopicki, Marek and Zurek, Sebastian and Stolkin, Rustam and Moerwald, Thomas and Wyatt, Jeremy L |journal=Autonomous Robots |volume=41 |number=5 |pages=1061–1082 |year=2017 |publisher=Springer |doi=10.1007/s10514-016-9571-3|doi-access=free }}</ref> The error between the real system and the forward model can be measured.

There are many techniques available to create a forward model: [[ordinary differential equation]]s is the classical one which is used in [[physics engine]]s like [[Box2D]]. A more recent technique is a [[neural network]] for creating the forward model.<ref>{{cite conference |title=Model predictive neural control of a high-fidelity helicopter model |author=Eric Wan and Antonio Baptista and Magnus Carlsson and Richard Kiebutz and Yinglong Zhang and Alexander Bogdanov |year=2001 |publisher=American Institute of Aeronautics and Astronautics |conference={AIAA |doi=10.2514/6.2001-4164}}</ref>