Learning to Control Known Feedback Linearizable Systems From Demonstrations

this article, we revisit the problem of learning a stabilizing controller from a finite number of demonstrations by an expert. By first focusing on feedback linearizable systems, we show how to combine expert demonstrations into a stabilizing controller, provided that demonstration trajectories are sufficiently long and there are at least n + 1 of them, where n is the number of states of the system being controlled. When we have more than n + 1 demonstration trajectories, we discuss how to optimally choose the best n + 1 demonstrations to construct the stabilizing controller. We then extend these results to a class of systems that can be embedded into a higher dimensional system containing a chain of integrators. The feasibility of the proposed algorithm is demonstrated by applying it on a CrazyFlie 2.0 quadrotor.