Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
The complexity of probabilistic verification
Journal of the ACM (JACM)
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Stochastic Optimal Control: The Discrete-Time Case
Stochastic Optimal Control: The Discrete-Time Case
Computing Minimum and Maximum Reachability Times in Probabilistic Systems
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
Towars a Theory of Stochastic Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Reachability questions in piecewise deterministic Markov processes
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Bisimulation for general stochastic hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Polynomial stochastic hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
A toolbox of hamilton-jacobi solvers for analysis of nondeterministic continuous and hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
On reachability and minimum cost optimal control
Automatica (Journal of IFAC)
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Simulation of stochastic hybrid systems with switching and reflecting boundaries
Proceedings of the 40th Conference on Winter Simulation
Model-based probabilistic collision detection in autonomous driving
IEEE Transactions on Intelligent Transportation Systems
Safety analysis of sugar cataract development using stochastic hybrid systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Verification of discrete time stochastic hybrid systems: A stochastic reach-avoid decision problem
Automatica (Journal of IFAC)
Probabilistic invariance of mixed deterministic-stochastic dynamical systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
A stochastic games framework for verification and control of discrete time stochastic hybrid systems
Automatica (Journal of IFAC)
| Hi-index | 0.00 |
Stochastic hybrid system models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing algorithms for reachability analysis is challenging because of the interaction between the discrete and continuous stochastic dynamics. In this paper, we propose a probabilistic method for reachability analysis based on discrete approximations. The contribution of the paper is twofold. First, we show that reachability can be characterized as a viscosity solution of a system of coupled Hamilton-Jacobi-Bellman equations. Second, we present a numerical method for computing the solution based on discrete approximations and we show that this solution converges to the one for the original system as the discretization becomes finer. Finally, we illustrate the approach with a navigation benchmark that has been proposed for hybrid system verification.