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A stochastic games framework for verification and control of discrete time stochastic hybrid systems
A stochastic games framework for verification and control of discrete time stochastic hybrid systems
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.
- University of Oxford United Kingdom
- University of California, Berkeley United States
- École Polytechnique Fédérale de Lausanne Switzerland
- Delft University of Technology Netherlands
Microsoft Academic Graph classification: Optimal control Markov chain State space Mathematics Discrete time and continuous time Reachability Probabilistic logic Mathematical optimization Air traffic management Hybrid system
Electrical and Electronic Engineering, Control and Systems Engineering
Electrical and Electronic Engineering, Control and Systems Engineering
Microsoft Academic Graph classification: Optimal control Markov chain State space Mathematics Discrete time and continuous time Reachability Probabilistic logic Mathematical optimization Air traffic management Hybrid system
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).30 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).30 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
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- Natural Sciences and Engineering Research Council of Canada (NSERC)
- University of Oxford United Kingdom
- University of California, Berkeley United States
- École Polytechnique Fédérale de Lausanne Switzerland
- Delft University of Technology Netherlands
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.