Related papers: Approximate Stochastic Reachability for High Dimen…

Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…

This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state…

In this paper, we propose a data-driven robust safety verification framework for stochastic dynamical systems modeled as Markov decision processes with time-varying and uncertain transition probabilities. Rather than assuming access to the…

Density of the reachable states can help understand the risk of safety-critical systems, especially in situations when worst-case reachability is too conservative. Recent work provides a data-driven approach to compute the density…

Data-driven safety verification of robotic systems often relies on zonotopic reachability analysis due to its scalability and computational efficiency. However, for nonlinear systems, these methods can become overly conservative, especially…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

We present a scalable algorithm for learning parametric constraints in high dimensions from safe expert demonstrations. To reduce the ill-posedness of the constraint recovery problem, our method uses hit-and-run sampling to generate lower…

First-passage probability estimation of high-dimensional nonlinear stochastic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel…

Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic…

When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…

We present theory and algorithms for the computation of probability-weighted "keep-out" sets to assure probabilistically safe navigation in the presence of multiple rigid body obstacles with stochastic dynamics. Our forward stochastic…

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

Deep neural networks can be trained to be efficient and effective controllers for dynamical systems; however, the mechanics of deep neural networks are complex and difficult to guarantee. This work presents a general approach for providing…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…

We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…

This paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances. Our proposed distributionally robust safe policy maximizes the probability of a system remaining in a…

This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…

We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of…