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We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are…
In the context of Markov decision processes running in continuous time, one of the most intriguing challenges is the efficient approximation of finite horizon reachability objectives. A multitude of sophisticated model checking algorithms…
In many sampled-data applications, observers are designed based on approximately discretized models of continuous-time systems, where usually only the discretized system is analyzed in terms of its detectability. In this paper, we show that…
This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete…
We propose a simple yet effective divide-and-discard (DD) approach to guaranteed state estimation for nonlinear discrete-time systems. Our method iteratively subdivides interval enclosures of the state and propagates them forward in time…
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…
In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. Three different numerical treatments for temporal discretization are proposed to…
Hashing method maps similar data to binary hashcodes with smaller hamming distance, and it has received a broad attention due to its low storage cost and fast retrieval speed. However, the existing limitations make the present algorithms…
The paper addresses state estimation for linear discrete-time systems with binary (threshold) measurements. A Moving Horizon Estimation (MHE) approach is followed and different estimators, characterized by two different choices of the cost…
We analyze a semi-explicit time discretization scheme of first order for poro\-elasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled. The approach leads to a decoupling of…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
The time discretization of stochastic spectral fractional wave equation is studied by using the difference methods. Firstly, we exploit rectangle formula to get a low order time discretization, whose the strong convergence order is smaller…
This work proposes an algorithmic method to verify differential privacy for estimation mechanisms with performance guarantees. Differential privacy makes it hard to distinguish outputs of a mechanism produced by adjacent inputs. While…
In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
The stability analysis of model predictive control schemes without terminal constraints and/or costs has attracted considerable attention during the last years. We pursue a recently proposed approach which can be used to determine a…
We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a…
Auditing differential privacy has emerged as an important area of research that supports the design of privacy-preserving mechanisms. Privacy audits help to obtain empirical estimates of the privacy parameter, to expose flawed…
As control systems grow in complexity, abstraction-based methods have become essential for designing controllers with formal guarantees. However, a key limitation of these methods is their reliance on discrete-time models, typically…