Robust control in closed loops realised by fast signal transmission of infinite gain neurons

We show that using recurrent networks with finite time constants is not contradictory to arbitrary fast signal transmission in a closed loop with appropriate feedbacks. This surprising result is due to the occurrence of infinitely amplifying subloops, which we formally describe by differential inclusions. The theory then shows that the transmission speed depends crucially on the gain of the transfer function. Generalising the theoretical framework we demonstrate how to build efficient, fast and robust neuro-controllers with pre-specified performance by application to the benchmark problem of balancing the inverted pendulum