# Learning Stabilizable Dynamical Systems via Control Contraction Metrics

@article{Singh2019LearningSD,
title={Learning Stabilizable Dynamical Systems via Control Contraction Metrics},
author={Sumeet Singh and Vikas Sindhwani and Jean-Jacques E. Slotine and Marco Pavone},
journal={ArXiv},
year={2019},
volume={abs/1808.00113}
}
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. [...] Key Method 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…Expand
12 Citations
Learning Stabilizable Dynamical Systems via Control Contraction Metrics
• Computer Science
• WAFR
• 2018
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. Expand
Learning stabilizable nonlinear dynamics with contraction-based regularization
• Computer Science, Mathematics
• Int. J. Robotics Res.
• 2021
The results support the conjecture that the use of stabilizability constraints as a form of regularization can help prune the hypothesis space in a manner that is tailored to the downstream task of trajectory generation and feedback control, resulting in models that are not only dramatically better conditioned, but also data efficient. Expand
Learning-based Robust Motion Planning With Guaranteed Stability: A Contraction Theory Approach
• Computer Science, Engineering
• IEEE Robotics and Automation Letters
• 2021
This letter presents Learning-based Autonomous Guidance with RObustness and Stability guarantees (LAG-ROS), which provides machine learning-based nonlinear motion planners with formal robustness andExpand
Universal Adaptive Control for Uncertain Nonlinear Systems
• Computer Science
• ArXiv
• 2020
This work presents an adaptive control framework for nonlinear systems with unmatched uncertainties that addresses several of the limitations of existing methods through two key innovations, leveraging contraction theory and a new type of contraction metric that is able to track feasible trajectories generated by an adapting reference model. Expand
Contraction Metrics in Adaptive Nonlinear Control
• Computer Science, Engineering
• ArXiv
• 2019
This work uses contraction metrics to derive an adaptive controller for stabilizable nonlinear systems by constructing a distance-like function differentially rather than explicitly, and can be applied to a larger class of non linear systems as a result. Expand
Neural Stochastic Contraction Metrics for Learning-based Robust Control and Estimation
• Computer Science, Engineering
• ArXiv
• 2020
The NSCM framework allows autonomous agents to approximate optimal stable control and estimation policies in real-time, and outperforms existing nonlinear control and estimating techniques including the state-dependent Riccati equation, iterative LQR, EKF, and the deterministic neural contraction metric, as illustrated in simulation results. Expand
Adaptive Nonlinear Control With Contraction Metrics
• Computer Science
• IEEE Control Systems Letters
• 2021
This letter derives direct adaptive control algorithms for nonlinear systems nominally contracting in closed-loop, but subject to structured parametric uncertainty from methods based on feedback linearization or backstepping. Expand
Fitting a Linear Control Policy to Demonstrations with a Kalman Constraint
• Computer Science, Mathematics
• L4DC
• 2020
A heuristic method, based on the alternating direction method of multipliers (ADMM), is proposed, to approximately solve the problem of learning a linear control policy for a linear dynamical system from demonstrations of an expert regulating the system. Expand
Learning Dynamical Systems with Side Information
• Computer Science, Mathematics
• L4DC
• 2020
The overall learning methodology combines ideas from convex optimization, real algebra, dynamical systems, and functional approximation theory, and can potentially lead to new synergies between these areas. Expand

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