Sequential Stackelberg equilibria in two-person games
Journal of Optimization Theory and Applications
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Finitely additive stochastic games with Borel measurable payoffs
International Journal of Game Theory
Stochastic Optimal Control: The Discrete-Time Case
Stochastic Optimal Control: The Discrete-Time Case
Minimax Control of Discrete-Time Stochastic Systems
SIAM Journal on Control and Optimization
Towars a Theory of Stochastic Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems
Automatica (Journal of IFAC)
Three-Dimensional Kneed Bipedal Walking: A Hybrid Geometric Approach
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Safe and Secure Networked Control Systems under Denial-of-Service Attacks
HSCC '09 Proceedings of the 12th 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)
A stochastic reach-avoid problem with random obstacles
Proceedings of the 14th international conference on Hybrid systems: computation and control
Adaptive Gridding for Abstraction and Verification of Stochastic Hybrid Systems
QEST '11 Proceedings of the 2011 Eighth International Conference on Quantitative Evaluation of SysTems
Computational methods for reachability analysis of stochastic hybrid systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
A review of conflict detection and resolution modeling methods
IEEE Transactions on Intelligent Transportation Systems
A probabilistic approach to aircraft conflict detection
IEEE Transactions on Intelligent Transportation Systems
Aircraft conflict prediction in the presence of a spatially correlated wind field
IEEE Transactions on Intelligent Transportation Systems
Controllers for reachability specifications for hybrid systems
Automatica (Journal of IFAC)
| Hi-index | 22.14 |
We describe a framework for analyzing probabilistic reachability and safety problems for discrete time stochastic hybrid systems within a dynamic games setting. In particular, we consider finite horizon zero-sum stochastic games in which a control has the objective of reaching a target set while avoiding an unsafe set in the hybrid state space, and a rational adversary has the opposing objective. We derive an algorithm for computing the maximal probability of achieving the control objective, subject to the worst-case adversary behavior. From this algorithm, sufficient conditions of optimality are also derived for the synthesis of optimal control policies and worst-case disturbance strategies. These results are then specialized to the safety problem, in which the control objective is to remain within a safe set. We illustrate our modeling framework and computational approach using both a tutorial example with jump Markov dynamics and a practical application in the domain of air traffic management.