Learning Control-Oriented Dynamical Structure from Data
- URL: http://arxiv.org/abs/2302.02529v2
- Date: Sat, 24 Jun 2023 03:24:09 GMT
- Title: Learning Control-Oriented Dynamical Structure from Data
- Authors: Spencer M. Richards, Jean-Jacques Slotine, Navid Azizan, Marco Pavone
- Abstract summary: We discuss a state-dependent nonlinear tracking controller formulation for general nonlinear control-affine systems.
We empirically demonstrate the efficacy of learned versions of this controller in stable trajectory tracking.
- Score: 25.316358215670274
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Even for known nonlinear dynamical systems, feedback controller synthesis is
a difficult problem that often requires leveraging the particular structure of
the dynamics to induce a stable closed-loop system. For general nonlinear
models, including those fit to data, there may not be enough known structure to
reliably synthesize a stabilizing feedback controller. In this paper, we
discuss a state-dependent nonlinear tracking controller formulation based on a
state-dependent Riccati equation for general nonlinear control-affine systems.
This formulation depends on a nonlinear factorization of the system of vector
fields defining the control-affine dynamics, which always exists under mild
smoothness assumptions. We propose a method for learning this factorization
from a finite set of data. On a variety of simulated nonlinear dynamical
systems, we empirically demonstrate the efficacy of learned versions of this
controller in stable trajectory tracking. Alongside our learning method, we
evaluate recent ideas in jointly learning a controller and stabilizability
certificate for known dynamical systems; we show experimentally that such
methods can be frail in comparison.
Related papers
- Learning Controlled Stochastic Differential Equations [61.82896036131116]
This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion.
We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity.
Our method is available as an open-source Python library.
arXiv Detail & Related papers (2024-11-04T11:09:58Z) - 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) - Capturing Actionable Dynamics with Structured Latent Ordinary
Differential Equations [68.62843292346813]
We propose a structured latent ODE model that captures system input variations within its latent representation.
Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
arXiv Detail & Related papers (2022-02-25T20:00:56Z) - Neural Koopman Lyapunov Control [0.0]
We propose a framework to identify and construct stabilizable bilinear control systems and its associated observables from data.
Our proposed approach provides provable guarantees of global stability for the nonlinear control systems with unknown dynamics.
arXiv Detail & Related papers (2022-01-13T17:38:09Z) - Learning over All Stabilizing Nonlinear Controllers for a
Partially-Observed Linear System [4.3012765978447565]
We propose a parameterization of nonlinear output feedback controllers for linear dynamical systems.
Our approach guarantees the closed-loop stability of partially observable linear dynamical systems without requiring any constraints to be satisfied.
arXiv Detail & Related papers (2021-12-08T10:43:47Z) - Sparsity in Partially Controllable Linear Systems [56.142264865866636]
We study partially controllable linear dynamical systems specified by an underlying sparsity pattern.
Our results characterize those state variables which are irrelevant for optimal control.
arXiv Detail & Related papers (2021-10-12T16:41:47Z) - 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) - Gaussian Process-based Min-norm Stabilizing Controller for
Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
We propose a novel compound kernel that captures the control-affine nature of the problem.
We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
arXiv Detail & Related papers (2020-11-14T01:27:32Z) - Neural Identification for Control [30.91037635723668]
The proposed method relies on the Lyapunov stability theory to generate a stable closed-loop dynamics hypothesis and corresponding control law.
We demonstrate our method on various nonlinear control problems such as n-link pendulum balancing and trajectory tracking, pendulum on cart balancing, and wheeled vehicle path following.
arXiv Detail & Related papers (2020-09-24T16:17:44Z) - Active Learning for Nonlinear System Identification with Guarantees [102.43355665393067]
We study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs.
We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data.
We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression.
arXiv Detail & Related papers (2020-06-18T04:54:11Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.