• shareshare
  • link
  • cite
  • add
auto_awesome_motion View all 2 versions
Publication . Other literature type . Article . 2013

A stochastic games framework for verification and control of discrete time stochastic hybrid systems

Jerry Ding; Maryam Kamgarpour; Sean Summers; Alessandro Abate; John Lygeros; Claire J. Tomlin;
Closed Access
Published: 01 Sep 2013
Country: Switzerland

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.

Subjects by Vocabulary

Microsoft Academic Graph classification: Mathematics Probabilistic logic State space Discrete time and continuous time Air traffic management Reachability Optimal control Hybrid system Markov chain Mathematical optimization


Electrical and Electronic Engineering, Control and Systems Engineering

Funded by
Modeling, verification and control of complex systems: From foundations to power network applications
  • Funder: European Commission (EC)
  • Project Code: 257005
  • Funding stream: FP7 | SP1 | ICT
  • Funder: Natural Sciences and Engineering Research Council of Canada (NSERC)
A Novel Mathematical Framework for the Modelling and the Analysis of Transportation Networks (MANTRAS)
  • Funder: European Commission (EC)
  • Project Code: 249295
  • Funding stream: FP7 | SP3 | PEOPLE
Related to Research communities
Social Science and Humanities