Data-driven control for SISO feedback linearizable systems with unknown control gain

In this paper we consider the problem of controlling an unknown system without making use of prior data or training. By relying on a feedback linearizability assumption we show how, based on prior ideas by Fliess and co-workers on model-free control, it is possible to accomplish such objective. The key idea is to learn a model that is only valid at the current state and re-learn this model as time progresses. Since this requires learning two real numbers rather than functions, it results in an approach quite different from: 1) deep learning since it requires no prior data neither large amounts of data; 2) reinforcement learning since it converges much faster and does not suffer from the curse of dimensionality.