Applications of Stochastic Reachability

  • Luminita Manuela Bujorianu
Chapter
Part of the Communications and Control Engineering book series (CCE)

Abstract

This chapter aims to give a flavour of the range of stochastic reachability applications. A list (that is not exhaustive) with appropriate references is given. The chapter is concerned only with the applications in air traffic management and biology. For air traffic management we summarise the existing work on using stochastic reachability for conflict detection and conflict resolution. The aircraft conflicts represent situations where an aircraft comes too close to another aircraft or enters a forbidden zone. The application of stochastic reachability to conflict detection is quite clear and it will have a great impact in the context of free flight. For conflict resolution, stochastic reachability analysis alone is not enough. It should be combined with other control techniques like model predictive control, path planning or randomised algorithms. Stochastic reachability has proved to be a powerful tool for the analysis of biological systems. These systems are inherently noisy and have hybrid behaviour, and most of their analysis problems could be modelled in the framework of stochastic reachability.

Keywords

Sugar Bacillus Cataract 

References

  1. 30.
    Blom, H.A.P., Bakker, G.J., Krystul, J., Klompstra, M.B., Obbink, B.K.: Free flight collision risk estimation by sequential Monte Carlo simulation. In: Cassandras, C.G., Lygeros, J. (eds.) Stochastic Hybrid Systems; Recent Developments and Research Trends. Taylor & Francis/CRC Press, London/Boca Raton (2007) (Chap. 10) Google Scholar
  2. 31.
    Blom, H.A.P., Bakker, G.J.: Conflict probability and incrossing probability in air traffic management. In: Proc. of the 41st IEEE Conference on Decision and Control 3, 2421–2426 (2002) Google Scholar
  3. 32.
    Blom, H.A.P., Stroeve, S.H., Everdij, M.H.C., Van der Park, M.N.J.: Collision risk modelling of air traffic. In: Proc. of European Control Conference (2003) Google Scholar
  4. 80.
    El-Samad, H., Fazel, M., Liu, X., Papachristodoulou, A., Prajna, S.: Stochastic reachability analysis in complex biological networks. In: Proc. of the IEEE American Control Conference (2006) (6 pp.) Google Scholar
  5. 84.
    Everdij, M., Blom, H.A.P.: Bias and uncertainty in accident risk assessment. NLR Report CR-2002-137, National Laboratory of Aerospace NLR (2002) Google Scholar
  6. 85.
    Everdij, M., Blom, H.A.P.: Modelling hybrid state Markov processes through dynamically and stochastically coloured Petri nets. HYBRIDGE Deliverable D2.4 (2005). Available on [126] Google Scholar
  7. 86.
    Everdij, M., Blom, H.A.P., Stroeve, S.H.: Structured assessment of bias and uncertainty in Monte Carlo simulated ask risk. In: Proc. of the 8th Int. Conf. on Probabilistic Safety Assessment and Management (2006) Google Scholar
  8. 123.
    Hu, J., Wu, W., Sastry, S.: Modeling subtilin production in Bacillus subtilis using stochastic hybrid systems. In: Alur, R., Pappas, G. (eds.) Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, vol. 2993, pp. 163–166. Springer, Berlin (2004) Google Scholar
  9. 124.
    Hu, J., Prandini, M., Sastry, S.: Probabilistic safety analysis in three dimensional aircraft flight. In: Proc. of the 42nd IEEE Conference on Decision and Control, pp. 5335–5340 (2003) Google Scholar
  10. 125.
    Hu, J., Prandini, M., Sastry, S.: Aircraft conflict prediction in the presence of a spatially correlated wind field. IEEE Trans. Intell. Transp. Syst. 6(3), 326–340 (2005) CrossRefGoogle Scholar
  11. 126.
    European Commission HYBRIDGE project: Distributed control and stochastic analysis of hybrid systems supporting safety critical real-time system design. www.nlr.nl/public/hosted-sites/hybridge/
  12. 127.
    Hu, J., Prandini, M.: Aircraft conflict detection: a method for computing the probability of conflict based on Markov chain approximation. In: Proc. of the European Control Conference (2003) Google Scholar
  13. 133.
    European Commission iFLY project: Safety, complexity and responsibility based design and validation of highly automated air traffic management. http://ifly.nlr.nl/
  14. 172.
    Lymperopoulos, I., Lygeros, J.: Sequential Monte Carlo methods for multi-aircraft trajectory prediction in air traffic management. Int. J. Adapt. Control Signal Process. 24, 830–849 (2010) CrossRefMATHMathSciNetGoogle Scholar
  15. 173.
    Lymperopoulos, I., Lygeros, J.: Improved multi-aircraft ground trajectory prediction for air traffic control. J. Guid. Control Dyn. 33, 347–362 (2010) CrossRefGoogle Scholar
  16. 174.
    Lymperopoulos, I., Lygeros, J.: Improved ground trajectory prediction by multi-aircraft track fusion for air traffic control. In: AIAA Guidance, Navigation and Control Conference and Exhibit AIAA-2009-5784 (2009) Google Scholar
  17. 175.
    Lymperopoulos, I., Lygeros, J.: Adaptive aircraft trajectory prediction using particle filters. In: AIAA Guidance, Navigation and Control Conference and Exhibit (2009) Google Scholar
  18. 197.
    Prandini, M., Hu, J.: Applications of reachability analysis for stochastic hybrid systems to aircraft conflict prediction. IEEE Trans. Autom. Control 54(4), 913–917 (2009) CrossRefMathSciNetGoogle Scholar
  19. 201.
    Riley, D.: Modeling, simulation, and verification of biochemical processes using stochastic hybrid systems. PhD Dissertation (2009) Google Scholar
  20. 202.
    Riley, D., Koutsoukos, X., Riley, K.: Reachability analysis of a biodiesel production system using stochastic hybrid systems. In: Proc. of 15th IEEE Mediterranean Conference on Control and Automation (2007) Google Scholar
  21. 203.
    Riley, D., Koutsoukos, X., Riley, K.: Safety analysis of sugar cataract developement using stochastic hybrid systems. In: Bemporad, A., Bicchi, A., Buttazzo, G.C. (eds.) Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, vol. 4416, pp. 758–761. Springer, Berlin (2007) CrossRefGoogle Scholar
  22. 204.
    Riley, D., Koutsoukos, X., Riley, K.: Reachability analysis for stochastic hybrid systems using multilevel splitting. In: Majumdar, R., Tabuada, P. (eds.) Hybrid Systems: Computation and Control, vol. 5469, pp. 460–464 (2009) CrossRefGoogle Scholar
  23. 226.
    Watkins, O.J.: Stochastic reachability, conflict detection, and air traffic management. Doctoral thesis (2004) Google Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • Luminita Manuela Bujorianu
    • 1
  1. 1.School of MathematicsUniversity of ManchesterManchesterUK

Personalised recommendations