Related papers: Guaranteed approximations of arbitrarily quantifie…
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
Reachability analysis evaluates system safety, by identifying the set of states a system may evolve within over a finite time horizon. In contrast to model-based reachability analysis, data-driven reachability analysis estimates reachable…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…
This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and…
Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…
We are concerned with three types of uncertainties: probabilistic, possibilitistic and interval. By using possibility and necessity measures as an Interval Valued Probability Measure (IVPM), we present IVPM's interval expected values whose…
We present two data-driven methods for estimating reachable sets with probabilistic guarantees. Both methods make use of a probabilistic formulation allowing for a formal definition of a data-driven reachable set approximation that is…
Many problems in robust control and motion planning can be reduced to either find a sound approximation of the solution space determined by a set of nonlinear inequalities, or to the ``guaranteed tuning problem'' as defined by Jaulin and…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
We consider discrete optimization problems with interval uncertatinty of objective function coefficients. The interval uncertainty models measurements errors. A pos\-sible optimal solution is a solution that is optimal for some possible…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
This paper considers the tracking control problem for an unknown nonlinear system with time-varying bounded disturbance subjected to a prescribed performance and input constraints. When performance and input constraints are specified…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…