Related papers: Reach-avoid Verification using Lyapunov Densities
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…
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…
Stability, reachability, and safety are crucial properties of dynamical systems. While verification and control synthesis of reach-avoid-stay objectives can be effectively handled by abstraction-based formal methods, such approaches can be…
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…
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…
This paper investigates necessary and sufficient barrier-like conditions for infinite-horizon safety and reach-avoid verification of stochastic discrete-time systems, derived via a relaxation of the Bellman equations. Unlike prior…
Stability and safety are two important aspects in safety-critical control of dynamical systems. It has been a well established fact in control theory that stability properties can be characterized by Lyapunov functions. Reachability…
In this paper we propose a novel semi-definite programming approach that solves reach-avoid problems over open (i.e., not bounded a priori) time horizons for dynamical systems modeled by polynomial stochastic differential equations. The…
Forward reachability analysis is the predominant approach for verifying reach-avoid properties in neural feedback systems (dynamical systems controlled by neural networks). This dominance stems from the limited scalability of existing…
In this paper we study reachability verification problems of stochastic discrete-time dynamical systems over the infinite time horizon. The reachability verification of interest in this paper is to certify specified lower and upper bounds…
We consider the maximal reach-avoid probability to a target in finite horizon for semi-Markov decision processes with time-varying obstacles. Since the variance of the obstacle set, the model \eqref{Model} is non-homogeneous. To overcome…
In this paper, we address the stochastic reach-avoid problem for linear systems with additive stochastic uncertainty. We seek to compute the maximum probability that the states remain in a safe set over a finite time horizon and reach a…
In this paper we propose sufficient conditions to synthesizing reach-avoid controllers for deterministic systems modelled by ordinary differential equations and stochastic systems modeled by stochastic differential equations based on the…
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…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…
This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
This paper considers a sampling-based approach to stability verification for piecewise continuous nonlinear systems via Lyapunov functions. Depending on the system dynamics, the candidate Lyapunov function and the set of initial states of…
Model-based reinforcement learning seeks to simultaneously learn the dynamics of an unknown stochastic environment and synthesise an optimal policy for acting in it. Ensuring the safety and robustness of sequential decisions made through a…
Providing finite-time probabilistic safety and reach-avoid guarantees is crucial for safety-critical stochastic systems. Existing state-of-the-art barrier methods often rely on a restrictive boundedness assumption for auxiliary functions,…
We examine Lagrangian techniques for computing underapproximations of finite-time horizon, stochastic reach-avoid level-sets for discrete-time, nonlinear systems. We use the concept of reachability of a target tube in the control literature…