Learning Stabilizable Dynamical Systems via Control Contraction Metrics

TL;DR

This paper introduces a new control-theoretic regularizer for learning stabilizable nonlinear dynamical systems, enhancing trajectory control in robotics with improved stability and performance, especially in data-scarce scenarios.

Contribution

It develops a semi-supervised learning algorithm based on contraction theory to ensure learned dynamics are stabilizable, which is novel in combining control theory with statistical learning.

Findings

Improved trajectory tracking in simulated quadrotor.

Enhanced model stability with fewer demonstration data.

Control-theoretic regularization outperforms traditional regression.

Abstract

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.