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Related papers: Reach-avoid Verification using Lyapunov Densities

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Emerging applications in robotics and autonomous systems, such as autonomous driving and robotic surgery, often involve critical safety constraints that must be satisfied even when information about system models is limited. In this regard,…

Robotics · Computer Science 2020-02-25 Subin Huh , Insoon Yang

In this paper, we compare several representative barrier-like conditions from the literature for infinite-horizon reach-avoid verification of stochastic discrete-time systems. Our comparison examines both their theoretical properties and…

Systems and Control · Electrical Eng. & Systems 2025-12-08 Zhipeng Cao , Peixin Wang , Luke Ong , Đorđe Žikelić , Dominik Wagner , Bai Xue

We initiate a formal study on the use of low-dimensional latent representations of dynamical systems for verifiable control synthesis. Our main goal is to enable the application of verification techniques -- such as Lyapunov or barrier…

Systems and Control · Electrical Eng. & Systems 2026-01-08 Paul Lutkus , Kaiyuan Wang , Lars Lindemann , Stephen Tu

We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results concerning existence and uniqueness are obtained under…

Probability · Mathematics 2019-11-19 Sima Mehri , Wilhelm Stannat

Markov Decision Processes (MDPs) are a classical model for decision making in the presence of uncertainty. Often they are viewed as state transformers with planning objectives defined with respect to paths over MDP states. An increasingly…

Artificial Intelligence · Computer Science 2024-05-08 S. Akshay , Krishnendu Chatterjee , Tobias Meggendorfer , Đorđe Žikelić

We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and…

Machine Learning · Computer Science 2022-11-30 Đorđe Žikelić , Mathias Lechner , Thomas A. Henzinger , Krishnendu Chatterjee

Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…

Systems and Control · Electrical Eng. & Systems 2020-11-17 Niklas Kochdumper , Bastian Schürmann , Matthias Althoff

Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm…

Numerical Analysis · Mathematics 2024-02-23 Mark Wetzlinger , Niklas Kochdumper , Stanley Bak , Matthias Althoff

This paper concerns the problem of reachability of a given state for a multiagent control system in $\mathbb{R}^d$. In such a system, at every time each agent can choose his/her velocity which depends both on his/her position and on the…

Optimization and Control · Mathematics 2026-01-01 Giulia Cavagnari , Marc Quincampoix

We prove a converse Lyapunov theorem for boundedness of reachability sets for a general class of control systems whose flow is Lipschitz continuous on compact intervals with respect to trajectory-dominated inputs. We show that this…

Optimization and Control · Mathematics 2026-03-05 Patrick Bachmann , Andrii Mironchenko

A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage…

We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by…

Optimization and Control · Mathematics 2015-06-11 Nikolaos Kariotoglou , Maryam Kamgarpour , Tyler H. Summers , John Lygeros

In this work, we consider the fundamental problem of reachability analysis over imperative programs with real variables. The reachability property requires that a program can reach certain target states during its execution. Previous works…

Programming Languages · Computer Science 2020-07-29 Ali Asadi , Krishnendu Chatterjee , Hongfei Fu , Amir Kafshdar Goharshady , Mohammad Mahdavi

One of the most fundamental problems in Markov decision processes is analysis and control synthesis for safety and reachability specifications. We consider the stochastic reach-avoid problem, in which the objective is to synthesize a…

Optimization and Control · Mathematics 2017-10-09 Nikolaos Kariotoglou , Maryam Kamgarpour , Tyler Summers , John Lygeros

Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…

Optimization and Control · Mathematics 2020-12-01 Abraham P. Vinod , Meeko M. K. Oishi

We present a general framework for applying machine-learning algorithms to the verification of Markov decision processes (MDPs). The primary goal of these techniques is to improve performance by avoiding an exhaustive exploration of the…

This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…

Systems and Control · Computer Science 2019-06-05 Yuzhen Qin , Ming Cao , Brian D. O. Anderson

This paper introduces harmonic control Lyapunov barrier functions (harmonic CLBF) that aid in constrained control problems such as reach-avoid problems. Harmonic CLBFs exploit the maximum principle that harmonic functions satisfy to encode…

Optimization and Control · Mathematics 2024-03-27 Amartya Mukherjee , Ruikun Zhou , Haocheng Chang , Jun Liu

In this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective. Preceding approaches to solving these reachability problems are either confined to the deterministic setting…

Optimization and Control · Mathematics 2017-11-27 Peyman Mohajerin Esfahani , Debasish Chatterjee , John Lygeros

In this work, we present a novel Koopman spectrum-based reachability verification method for nonlinear systems. Contrary to conventional methods that focus on characterizing all potential states of a dynamical system over a presupposed time…

Systems and Control · Electrical Eng. & Systems 2025-12-01 Jianqiang Ding , Shankar A. Deka