Related papers: Data-driven Discovery of Invariant Measures
Data-driven control offers a powerful alternative to traditional model-based methods, particularly when accurate system models are unavailable or prohibitively complex. While existing data-driven control methods primarily aim to construct…
Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…
The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable…
Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
Chaotic systems make long-horizon forecasts difficult because small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, neural operators trained to minimize squared error losses, while…
We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown flow map of the underlying system. It employs the idea of…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
The numerical simulation of realistic reactive flows is a major challenge due to the stiffness and high dimension of the corresponding kinetic differential equations. Manifold-based model reduction techniques address this problem by…
In Willems' behavioral systems theory, a dynamical system is identified with the set of all trajectories compatible with its laws of motion. In the linear time-invariant setting this trajectory set is a linear subspace, and its algebraic…
We present a noise guided trajectory based system identification method for inferring the dynamical structure from observation generated by stochastic differential equations. Our method can handle various kinds of noise, including the case…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents.…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…
In the first part of the paper, we consider a discrete-time stochastic control system. We show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the…
For a discrete-time linear system, we use data from a single open-loop experiment to design directly a feedback controller enforcing that a given (polyhedral) set of the state is invariant and given (polyhedral) constraints on the control…
This paper proposes a data-driven control framework to regulate an unknown, stochastic linear dynamical system to the solution of a (stochastic) convex optimization problem. Despite the centrality of this problem, most of the available…
This paper presents the design of an extremum seeking controller based on sliding modes and cyclic search for real-time optimization of non-linear multivariable dynamic systems. These systems have arbitrary relative degree, compensated by…