Related papers: Guaranteed approximations of arbitrarily quantifie…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
There exist many Runge-Kutta methods (explicit or implicit), more or less adapted to specific problems. Some of them have interesting properties, such as stability for stiff problems or symplectic capability for problems with energy…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner…
Designing provably safe control is a core problem in trustworthy autonomy. However, most prior work in this regard assumes either that the system dynamics are known or deterministic, or that the state and action space are finite,…
We study an optimization-based approach to construct statistically accurate confidence intervals for simulation performance measures under nonparametric input uncertainty. This approach computes confidence bounds from simulation runs driven…
Intercepting dynamic objects in uncertain environments involves a significant unresolved challenge in modern robotic systems. Current control approaches rely solely on estimated information, and results lack guarantees of robustness and…
The safety region of operation of a system is the subset of allowed outputs for which no undesirable outcome would occur. Knowing if a system would ever leave its safety regions of operation is important information for the planning and…
Reachability computations that rely on learned or estimated models require calibration in order to uphold confidence about their guarantees. Calibration generally involves sampling scenarios inside the reachable set. However, producing…
We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an…
In imaging inverse problems, one seeks to recover an image from missing/corrupted measurements. Because such problems are ill-posed, there is great motivation to quantify the uncertainty induced by the measurement-and-recovery process.…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
The paper is concerned with space-time IgA approximations of parabolic initial-boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of IgA approximations and investigate their…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…
This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…
In various applications the search for certificates for certain properties (e.g., stability of dynamical systems, program termination) can be formulated as a quantified constraint solving problem with quantifier prefix exists-forall. In…
We design a general framework for answering adaptive statistical queries that focuses on providing explicit confidence intervals along with point estimates. Prior work in this area has either focused on providing tight confidence intervals…