Related papers: Data driven synthesis of provable invariant sets v…
Willems' fundamental lemma and system level synthesis both characterize a linear dynamic system by its input/output sequences. In this work, we extend the application of the fundamental lemma from deterministic to uncertain LTI systems and…
Private synthetic data sharing is preferred as it keeps the distribution and nuances of original data compared to summary statistics. The state-of-the-art methods adopt a select-measure-generate paradigm, but measuring large domain…
A procedure and theoretical results are presented for the problem of determining a minimal robust positively invariant (RPI) set for a linear discrete-time system subject to unknown, bounded disturbances. The procedure computes, via the…
The control of complex systems faces a trade-off between high performance and safety guarantees, which in particular restricts the application of learning-based methods to safety-critical systems. A recently proposed framework to address…
In this paper we develop a new data-driven closure approximation method to compute the statistical properties of quantities of interest in high-dimensional stochastic dynamical systems. The new method relies on estimating conditional…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…
Dimensional analysis is one of the most fundamental tools for understanding physical systems. However, the construction of dimensionless variables, as guided by the Buckingham-$\pi$ theorem, is not uniquely determined. Here, we introduce…
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
Control invariant set is critical for guaranteeing safe control and the problem of computing control invariant set for linear discrete-time system is revisited in this paper by using a data-driven approach. Specifically, sample points on…
Inspired by a concrete industry problem we consider the input synthesis problem for hybrid systems: given a hybrid system that is subject to input from outside (also called disturbance or noise), find an input sequence that steers the…
By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $\Sigma$ and a stochastic memoryless map $\Psi$. After that, we extend the result to the class of large…
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…
We formulate a novel approach to solve a class of stochastic problems, referred to as data-consistent inverse (DCI) problems, which involve the characterization of a probability measure on the parameters of a computational model whose…
In this paper, we consider the problem of invariant set computation for black-box switched linear systems using merely a finite set of observations of system trajectories. In particular, this paper focuses on polyhedral invariant sets. We…
Data-driven control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, besides measurement noise, stochastic disturbances might also directly affect…
Designing the terminal ingredients of direct data-driven predictive control presents challenges due to its reliance on an implicit, non-minimal input-output data-driven representation. By considering the class of constrained LTI systems…
The goal of this paper is to develop data-driven control design and evaluation strategies based on linear matrix inequalities (LMIs) and dynamic programming. We consider deterministic discrete-time LTI systems, where the system model is…
A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples appear to shift \emph{along} the support of the data…
This paper demonstrates how to use generative models trained for image synthesis as tools for visual data mining. Our insight is that since contemporary generative models learn an accurate representation of their training data, we can use…