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Learning Stabilizable Dynamical Systems via Control Contraction Metrics

EasyChair Preprint no. 750

16 pagesDate: January 22, 2019


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.

Keyphrases: contraction theory, control theoretic regularizer, dynamic learning, dynamics modeling, Kernel Hilbert space, Learning from Demonstration, machine learning, model-based reinforcement learning, optimal control and optimization, simulated planar quadrotor system, stabilizable dynamical system, statistical learning, Underactuated mechanical system

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
  author = {Sumeet Singh and Vikas Sindhwani and Jean-Jacques Slotine and Marco Pavone},
  title = {Learning Stabilizable Dynamical Systems via Control Contraction Metrics},
  howpublished = {EasyChair Preprint no. 750},
  doi = {10.29007/jz9w},
  year = {EasyChair, 2019}}
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