Learning a Forward Model of a Reflex

We develop a systems theoretical treatment of a behavioural system that interacts with its environment in a closed loop situation such that its motor actionsinfluence its sensor inputs. The simplest form of a feedback is a reflex. Reflexes occur always "too late"; i.e., only after a (unpleasant, painful,dangerous) reflex-eliciting sensor event has occurred. This defines an objective problem which can be solved if another sensor input exists which can predict the primary reflex and can generate an earlier reaction. In contrast to previous approaches, our linear learning algorithm allowsfor an analytical proof that this system learns to apply feedforward controlwith the result that slow feedback loops are replaced by their equivalent feed-forward controller creating a forward model. In other words, learning turns the reactive system into a proactive system. By means of a robot implementation we demonstrate the applicability of the theoretical results which can be used in a variety of different areas in physics and engineering.