Latest revision as of 10:21, 16 February 2021

Abstract

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.

Original document

The different versions of the original document can be found in:

• http://dx.doi.org/10.1016/j.automatica.2013.05.025

• https://api.elsevier.com/content/article/PII:S0005109813003087?httpAccept=text/xml,

https://api.elsevier.com/content/article/PII:S0005109813003087?httpAccept=text/plain,

http://dx.doi.org/10.1016/j.automatica.2013.05.025

• https://www.sciencedirect.com/science/article/pii/S0005109813003087,

https://dialnet.unirioja.es/servlet/articulo?codigo=4718490,

https://core.ac.uk/display/22694983,

https://www.cs.ox.ac.uk/people/alessandro.abate/publications/DKSALT13.pdf,

https://dblp.uni-trier.de/db/journals/automatica/automatica49.html#DingKSALT13,

http://www.cs.ox.ac.uk/people/alessandro.abate/publications/DKSALT13.pdf,

https://doi.org/10.1016/j.automatica.2013.05.025,

https://academic.microsoft.com/#/detail/2154136656