Related papers: Learning Stabilizable Deep Dynamics Models

Learning Stabilizable Deep Dynamics Models

URL: http://arxiv.org/abs/2203.09710v1
Date: Fri, 18 Mar 2022 03:09:24 GMT
Title: Learning Stabilizable Deep Dynamics Models
Authors: Kenji Kashima, Ryota Yoshiuchi, Yu Kawano
Abstract summary: We propose a new method for learning the dynamics of input-affine control systems. An important feature is that a stabilizing controller and control Lyapunov function of the learned model are obtained as well. The proposed method can also be applied to solving Hamilton-Jacobi inequalities.
Score: 1.75320459412718
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global exponential stability using neural networks. In this paper, we propose a new method for learning the dynamics of input-affine control systems. An important feature is that a stabilizing controller and control Lyapunov function of the learned model are obtained as well. Moreover, the proposed method can also be applied to solving Hamilton-Jacobi inequalities. The usefulness of the proposed method is examined through numerical examples.

Related papers

Learning Deep Dissipative Dynamics [5.862431328401459]
Dissipativity is a crucial indicator for dynamical systems that generalizes stability and input-output stability. We propose a differentiable projection that transforms any dynamics represented by neural networks into dissipative ones. Our method strictly guarantees stability, input-output stability, and energy conservation of trained dynamical systems.
arXiv Detail & Related papers (2024-08-21T09:44:43Z)
Data-Driven Control with Inherent Lyapunov Stability [3.695480271934742]
We propose Control with Inherent Lyapunov Stability (CoILS) as a method for jointly learning parametric representations of a nonlinear dynamics model and a stabilizing controller from data. In addition to the stabilizability of the learned dynamics guaranteed by our novel construction, we show that the learned controller stabilizes the true dynamics under certain assumptions on the fidelity of the learned dynamics.
arXiv Detail & Related papers (2023-03-06T14:21:42Z)
ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
arXiv Detail & Related papers (2023-02-11T21:07:30Z)
On Robust Numerical Solver for ODE via Self-Attention Mechanism [82.95493796476767]
We explore training efficient and robust AI-enhanced numerical solvers with a small data size by mitigating intrinsic noise disturbances. We first analyze the ability of the self-attention mechanism to regulate noise in supervised learning and then propose a simple-yet-effective numerical solver, Attr, which introduces an additive self-attention mechanism to the numerical solution of differential equations.
arXiv Detail & Related papers (2023-02-05T01:39:21Z)
The least-control principle for learning at equilibrium [65.2998274413952]
We present a new principle for learning equilibrium recurrent neural networks, deep equilibrium models, or meta-learning. Our results shed light on how the brain might learn and offer new ways of approaching a broad class of machine learning problems.
arXiv Detail & Related papers (2022-07-04T11:27:08Z)
Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
arXiv Detail & Related papers (2021-11-02T10:51:42Z)
Supervised DKRC with Images for Offline System Identification [77.34726150561087]
Modern dynamical systems are becoming increasingly non-linear and complex. There is a need for a framework to model these systems in a compact and comprehensive representation for prediction and control. Our approach learns these basis functions using a supervised learning approach.
arXiv Detail & Related papers (2021-09-06T04:39:06Z)
Almost Surely Stable Deep Dynamics [4.199844472131922]
We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Our method works by embedding a Lyapunov neural network into the dynamic model, thereby inherently satisfying the stability criterion.
arXiv Detail & Related papers (2021-03-26T20:37:08Z)
DyNODE: Neural Ordinary Differential Equations for Dynamics Modeling in Continuous Control [0.0]
We present a novel approach that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. Results indicate that a simple DyNODE architecture when combined with an actor-critic reinforcement learning algorithm outperforms canonical neural networks.
arXiv Detail & Related papers (2020-09-09T12:56:58Z)
Learning Stable Deep Dynamics Models [91.90131512825504]
We propose an approach for learning dynamical systems that are guaranteed to be stable over the entire state space. We show that such learning systems are able to model simple dynamical systems and can be combined with additional deep generative models to learn complex dynamics.
arXiv Detail & Related papers (2020-01-17T00:04:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.