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Related papers: Reach-avoid Verification using Lyapunov Densities

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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…

Dynamical Systems · Mathematics 2022-06-03 Yiming Meng , Jun Liu

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…

Optimization and Control · Mathematics 2022-08-18 Bai Xue , Naijun Zhan , Martin Fränzle , Ji Wang , Wanwei Liu

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…

Dynamical Systems · Mathematics 2022-11-03 Yiming Meng , Jun Liu

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…

Systems and Control · Electrical Eng. & Systems 2025-10-22 Bai Xue

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…

Systems and Control · Electrical Eng. & Systems 2023-10-10 Taoran Wu , Dejin Ren , Shuyuan Zhang , Lei Wang , Bai Xue

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…

Systems and Control · Electrical Eng. & Systems 2026-01-06 Bai Xue

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…

Systems and Control · Electrical Eng. & Systems 2022-01-03 Yiming Meng , Yinan Li , Maxwell Fitzsimmons , Jun Liu

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…

Optimization and Control · Mathematics 2023-12-22 Bai Xue , Naijun Zhan , Martin Fränzle

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…

Artificial Intelligence · Computer Science 2026-01-14 Samuel I. Akinwande , Sydney M. Katz , Mykel J. Kochenderfer , Clark Barrett

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…

Systems and Control · Electrical Eng. & Systems 2023-02-21 Bai Xue

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…

Probability · Mathematics 2025-05-06 Yanyun Li , Xianping Guo

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…

Optimization and Control · Mathematics 2018-11-12 Hossein Sartipizadeh , Abraham P. Vinod , Behcet Acikmese , Meeko Oishi

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…

Systems and Control · Electrical Eng. & Systems 2023-03-01 Bai Xue

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…

Systems and Control · Electrical Eng. & Systems 2023-04-25 Jianqiang Ding , Taoran Wu , Yuping Qian , Lijun Zhang , Bai Xue

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…

Numerical Analysis · Mathematics 2020-08-06 Matthias Althoff

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…

Systems and Control · Computer Science 2015-09-11 Sofie Haesaert , Robert Babuska , Alessandro Abate

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…

Systems and Control · Computer Science 2016-09-02 Ruxandra Bobiti , Mircea Lazar

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…

Machine Learning · Computer Science 2023-10-04 Matthew Wicker , Luca Laurenti , Andrea Patane , Nicola Paoletti , Alessandro Abate , Marta Kwiatkowska

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,…

Systems and Control · Electrical Eng. & Systems 2026-05-12 Bai Xue , Luke Ong , Dominik Wagner , Peixin Wang

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…

Systems and Control · Computer Science 2017-04-13 Joseph D. Gleason , Abraham P. Vinod , Meeko. M. K. Oishi
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