Related papers: Learning Physically Consistent Lagrangian Control …

Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…

Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of…

Classical Hamiltonian systems with balanced loss and gain are considered in this review. A generic Hamiltonian formulation for systems with space-dependent balanced loss and gain is discussed. It is shown that the loss-gain terms may be…

Robotic systems operating in unstructured environments must operate under significant uncertainty arising from intermittent contacts, frictional variability, and unmodeled compliance. While recent model-free approaches have demonstrated…

We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long…

The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…

Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation…

In this paper, we propose novel learning frameworks to tackle optimal control problems by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. Applying the Pontryagin maximum principle to the…

Tracking Lagrangian coherent structures in dynamical systems is important for many applications such as oceanography and weather prediction. In this paper, we present a collaborative robotic control strategy designed to track stable and…

Controller design faces a trade-off between robustness and performance, and the reliability of linear controllers has caused many practitioners to focus on the former. However, there is renewed interest in improving system performance to…

Learning has propelled the cutting edge of performance in robotic control to new heights, allowing robots to operate with high performance in conditions that were previously unimaginable. The majority of the work, however, assumes that the…

We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…

Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations…

Lagrangian and Hamiltonian neural networks (LNNs and HNNs, respectively) encode strong inductive biases that allow them to outperform other models of physical systems significantly. However, these models have, thus far, mostly been limited…

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

The existence or not of pathologies in the context of Lagrangian theory is studied with the aid of Machine Learning algorithms. Using an example in the framework of classical mechanics, we make a proof of concept, that the construction of…

Lagrangian Neural Networks (LNNs) can learn arbitrary Lagrangians from trajectory data, but their unusual optimization objective leads to significant training instabilities that limit their application to complex systems. We propose several…

Reinforcement learning is commonly associated with training of reward-maximizing (or cost-minimizing) agents, in other words, controllers. It can be applied in model-free or model-based fashion, using a priori or online collected system…

Designing a stabilizing controller for nonlinear systems is a challenging task, especially for high-dimensional problems with unknown dynamics. Traditional reinforcement learning algorithms applied to stabilization tasks tend to drive the…

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…