  We propose a novel framework for learning stabilizable nonlinear dynamical
systems for continuous control tasks in robotics. The key idea is to develop a
new control-theoretic regularizer for dynamics fitting rooted in the notion of
stabilizability, which guarantees that the learned system can be accompanied by
a robust controller capable of stabilizing any open-loop trajectory that the
system may generate. By leveraging tools from contraction theory, statistical
learning, and convex optimization, we provide a general and tractable
semi-supervised algorithm to learn stabilizable dynamics, which can be applied
to complex underactuated systems. We validated the proposed algorithm on a
simulated planar quadrotor system and observed notably improved trajectory
generation and tracking performance with the control-theoretic regularized
model over models learned using traditional regression techniques, especially
when using a small number of demonstration examples. The results presented
illustrate the need to infuse standard model-based reinforcement learning
algorithms with concepts drawn from nonlinear control theory for improved
reliability.
