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Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…

We study the synthesis of a policy in a Markov decision process (MDP) following which an agent reaches a target state in the MDP while minimizing its total discounted cost. The problem combines a reachability criterion with a discounted…

Optimization and Control · Mathematics 2021-03-18 Yagiz Savas , Christos K. Verginis , Michael Hibbard , Ufuk Topcu

Given a Probabilistic Finite Automata (PFA), a set of states S, and an error threshold e > 0, our algorithm approximates the infimum probability (quantifying over all infinite words) that the automata reaches S. Our result contrasts with…

Logic in Computer Science · Computer Science 2010-09-21 Sergio Giro

We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic…

Systems and Control · Electrical Eng. & Systems 2024-12-05 Vignesh Sivaramakrishnan , Rosalyn A. Devonport , Murat Arcak , Meeko M. K. Oishi

In this paper we examine how Lagrangian techniques can be used to compute underapproximations and overapproximation of the finite-time horizon, stochastic reach-avoid level sets for discrete-time, nonlinear systems. This approach is…

Systems and Control · Computer Science 2018-10-17 Joseph D. Gleason , Abraham P. Vinod , Meeko M. K. Oishi

This study introduces a novel approach for learning mixtures of Markov chains, a critical process applicable to various fields, including healthcare and the analysis of web users. Existing research has identified a clear divide in…

Machine Learning · Computer Science 2024-05-27 Fabian Spaeh , Konstantinos Sotiropoulos , Charalampos E. Tsourakakis

In this paper we propose a convex programming based method to address a long-standing problem of inner-approximating backward reachable sets of state-constrained polynomial systems subject to time-varying uncertainties. The backward…

Optimization and Control · Mathematics 2019-06-12 Bai Xue , Martin Fränzle , Naijun Zhan

Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the…

Systems and Control · Electrical Eng. & Systems 2023-05-17 Taha Entesari , Mahyar Fazlyab

Time bounded reachability is a fundamental problem in model checking continuous-time Markov chains (CTMCs) and Markov decision processes (CTMDPs) for specifications in continuous stochastic logics. It can be computed by numerically solving…

Systems and Control · Electrical Eng. & Systems 2020-01-07 Mahmoud Salamati , Sadegh Soudjani , Rupak Majumdar

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

Optimization and Control · Mathematics 2026-04-16 Thomas Lew , Riccardo Bonalli , Marco Pavone

Computing tight over-approximation of reach sets of a controlled uncertain dynamical system is a common practice in verification of safety-critical cyber-physical systems (CPS). While several algorithms are available for this purpose, they…

Systems and Control · Electrical Eng. & Systems 2021-03-16 Shadi Haddad , Abhishek Halder

Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…

Numerical Analysis · Mathematics 2020-06-16 Peter Georg , Lars Grasedyck , Maren Klever , Rudolf Schill , Rainer Spang , Tilo Wettig

We study the approximation of a Markov chain on a reduced state space, for both discrete- and continuous-time Markov chains. In this context, we extend the existing theory of formal error bounds for the approximated transient distributions.…

Probability · Mathematics 2025-02-12 Fabian Michel , Markus Siegle

One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…

Logic in Computer Science · Computer Science 2009-09-29 D. Ravi , R. K. Shyamasundar

We study the worst-case communication complexity of distributed algorithms computing a path problem based on stationary distributions of random walks in a network $G$ with the caveat that $G$ is also the communication network. The problem…

Data Structures and Algorithms · Computer Science 2008-10-30 Rahul Sami , Andy Twigg

This paper investigates reachability analysis for max-plus linear systems (MPLS), an important class of dynamical systems that model synchronization and delay phenomena in timed discrete-event systems. We specifically focus on backward…

Systems and Control · Electrical Eng. & Systems 2026-01-16 Yuda Li , Shaoyuan Li , Xiang Yin

Handling uncertainty in model predictive control comes with various challenges, especially when considering state constraints under uncertainty. Most methods focus on either the conservative approach of robustly accounting for uncertainty…

Systems and Control · Electrical Eng. & Systems 2024-05-03 Michael Fink , Tim Brüdigam , Dirk Wollherr , Marion Leibold

We characterize the reachability probabilities in stochastic directed graphs by means of reinforcement learning methods. In particular, we show that the dynamics of the transition probabilities in a stochastic digraph can be modeled via a…

Artificial Intelligence · Computer Science 2022-02-28 Corrado Possieri , Mattia Frasca , Alessandro Rizzo

The cover time of a Markov chain on a finite state space is the expected time until all states are visited. We show that if the cover time of a discrete-time Markov chain with rational transitions probabilities is bounded, then it is a…

Probability · Mathematics 2024-01-30 John Sylvester

We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…

Optimization and Control · Mathematics 2021-03-16 Mohan Dantam , Amaury Pouly