Related papers: Reach-avoid Verification using Lyapunov Densities
We consider the initial-boundary value problem of a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities in a bounded domain $\Omega\subset\mathbb{R}^3$. Our first aim is to study…
In this paper we investigate repeated weak measurements,without post-selection, on a \emph{single copy} of an \emph{unknown} quantum state. The resulting random walk in state space is precisely characterised in terms of joint probabilities…
This work extends reachability analyses based on ellipsoidal techniques to Linear Time Invariant (LTI) systems subject to an integral quadratic constraint (IQC) between the past state and disturbance signals , interpreted as an input-output…
Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of…
This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…
We present a scalable underapproximation of the terminal hitting time stochastic reach-avoid probability at a given initial condition, for verification of high-dimensional stochastic LTI systems. While several approximation techniques have…
In many real-world reinforcement learning (RL) problems, besides optimizing the main objective function, an agent must concurrently avoid violating a number of constraints. In particular, besides optimizing performance it is crucial to…
Actuator malfunctions may have disastrous consequences for systems not designed to mitigate them. We focus on the loss of control authority over actuators, where some actuators are uncontrolled but remain fully capable. To counteract the…
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…
In the classical reach-avoid problem, autonomous mobile robots are tasked to reach a goal while avoiding obstacles. However, it is difficult to provide guarantees on the robot's performance when the obstacles form a narrow gap and the robot…
We present ProbReach, a tool for verifying probabilistic reachability for stochastic hybrid systems, i.e., computing the probability that the system reaches an unsafe region of the state space. In particular, ProbReach will compute an…
We present a sufficient condition that a pseudointegrable system has weak mixing property. The result is derived from Veech's weak mixing theorem for interval exhange [Veech, W.A. Amer.J.Math. {\bf 106}, 1331 (1984)]. We also present an…
The robust tracking and model following problem of linear discrete-time systems is investigated in this paper. An approach to design robust tracking controllers is proposed. The system is controlled to track dynamic inputs generated from a…
We obtain large deviation bounds for the measure of deviation sets associated to asymptotically additive and sub-additive potentials under some weak specification properties. In particular a large deviation principle is obtained in the case…
This paper is about reachability analysis in a restricted subclass of multi-pushdown automata. We assume that the control states of an automaton are partially ordered, and all transitions of an automaton go downwards with respect to the…
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 provides a systematic exposition of Lyapunov stability for compact sets in locally compact metric spaces. We explore foundational concepts, including neighborhoods of compact sets, invariant sets, and the properties of dynamical…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
Opacity is a property that captures security concerns in cyber-physical systems and its verification plays a significant role. This paper investigates the verifications of K-step and infinite-step weak and strong opacity for partially…
We develop new methods for constructing confidence sets and intervals in linear instrumental variables (IV) models based on tests that remain valid under weak identification and under heteroskedastic, autocorrelated, or clustered errors. In…