Related papers: Underapproximation of Reach-Avoid Sets for Discret…
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…
In this paper, we propose an approach for synthesizing provable reach-avoid controllers, which drive a deterministic system operating in an unknown environment to safely reach a desired target set. The approach falls within the reachability…
We study feedback controller synthesis for reach-avoid control of discrete-time, linear time-invariant (LTI) systems with Gaussian process and measurement noise. The problem is to compute a controller such that, with at least some required…
Digital control has become increasingly prevalent in modern systems, making continuous-time plants controlled by discrete-time (digital) controllers ubiquitous and crucial across industries, including aerospace, automotive, and…
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…
This paper studies finite-time safety and reach-avoid verification for stochastic discrete-time dynamical systems. The aim is to ascertain lower and upper bounds of the probability that, within a predefined finite-time horizon, a system…
Stability and safety are crucial in safety-critical control of dynamical systems. The reach-avoid-stay objectives for deterministic dynamical systems can be effectively handled by formal methods as well as Lyapunov methods with soundness…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
We propose a method to efficiently compute the forward stochastic reach (FSR) set and its probability measure for nonlinear systems with an affine disturbance input, that is stochastic and bounded. This method is applicable to systems with…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
In this note, we propose a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems. The class under consideration is the linear time-varying (LTV) class with integrable…
Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…
Analyzing and certifying stability and attractivity of nonlinear systems is a topic of research interest that has been extensively investigated by control theorists and engineers for many years. Despite that, accurately estimating domains…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
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 paper we propose novel optimization-based methods for verifying reach-avoid (or, eventuality) properties of continuous-time systems modelled by ordinary differential equations. Given a system, an initial set, a safe set and a target…
Reach-avoid analysis is fundamental to reasoning about the safety and goal-reaching behavior of dynamical systems, and serves as a foundation for specifying and verifying more complex control objectives. This paper introduces a reach-avoid…
Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial…
Stochastic dynamical systems have emerged as fundamental models across numerous application domains, providing powerful mathematical representations for capturing uncertain system behavior. In this paper, we address the problem of runtime…
We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…