Related papers: Interval Reachability Analysis using Second-Order …
In two phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
This paper provides an analytical methodology to compute the sensitivities with respect to system parameters for any second order hybrid Ordinary Differential Equation (ODE) system. The hybrid ODE system is characterized by discontinuities…
We propose a study of structured non-convex non-concave min-max problems which goes beyond standard first-order approaches. Inspired by the tight understanding established in recent works [Adil et al., 2022, Lin and Jordan, 2022b], we…
Global sensitivity analysis is often impracticable for complex and time demanding numerical models, as it requires a large number of runs. The reduced-basis approach provides a way to replace the original model by a much faster to run code.…
When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. To alleviate this linear…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped…
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…
We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from…
Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty.…
This paper presents algorithms for performing data-driven reachability analysis under temporal logic side information. In certain scenarios, the data-driven reachable sets of a robot can be prohibitively conservative due to the inherent…
Markov decision models (MDM) used in practical applications are most often less complex than the underlying `true' MDM. The reduction of model complexity is performed for several reasons. However, it is obviously of interest to know what…
The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…
We develop two notions of time-restricted sensitivity to initial conditions for measurable dynamical systems, where the time before divergence of a pair of paths is at most an asymptotically logarithmic function of a measure of their…
We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure…
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of…
We propose a novel sensitivity analysis framework for linear estimators with identification failures that can be viewed as seeing the wrong outcome distribution. Our approach measures the degree of identification failure through the change…
This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available.…
Natural policy gradient methods are popular reinforcement learning methods that improve the stability of policy gradient methods by utilizing second-order approximations to precondition the gradient with the inverse of the…