Solving Trajectory Optimization Problems by Influence Diagrams

  • Jiří Vomlel
  • Václav Kratochvíl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)


Influence diagrams are decision-theoretic extensions of Bayesian networks. In this paper we show how influence diagrams can be used to solve trajectory optimization problems. These problems are traditionally solved by methods of optimal control theory but influence diagrams offer an alternative that brings benefits over the traditional approaches. We describe how a trajectory optimization problem can be represented as an influence diagram. We illustrate our approach on two well-known trajectory optimization problems – the Brachistochrone Problem and the Goddard Problem. We present results of numerical experiments on these two problems, compare influence diagrams with optimal control methods, and discuss the benefits of influence diagrams.


Influence diagrams Probabilistic graphical models Optimal control theory Brachistochrone problem Goddard problem 


  1. Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957)zbMATHGoogle Scholar
  2. Bertsekas, D.P.: Dynamic Programming and Optimal Control, 2nd edn. Athena Scientific, Belmont (2000)Google Scholar
  3. Goddard, R.H.: A method for reaching extreme altitudes, volume 71(2). Smithsonian Miscellaneous Collections (1919)Google Scholar
  4. Howard, R.A., Matheson, J.E.: Influence diagrams. In: Howard, R.A., Matheson, J.E. (eds.) Readings on the Principles and Applications of Decision Analysis, vol. II, pp. 721–762. Strategic Decisions Group (1981)Google Scholar
  5. Jensen, F.: Bayesian Networks and Decision Graphs. Springer, New York (2001)CrossRefzbMATHGoogle Scholar
  6. Kratochvíl, V., Vomlel, J.: Influence diagrams for speed profile optimization. Int. J. Approximate Reasoning. (2016, in press).
  7. Miele, A.: A survey of the problem of optimizing flight paths of aircraft and missiles. In: Bellman, R. (ed.) Mathematical Optimization Techniques, pp. 3–32. University of California Press (1963)Google Scholar
  8. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann series in representation and reasoning. Morgan Kaufmann, Burlington (1988)Google Scholar
  9. Seywald, H., Cliff, E.M.: Goddard problem in presence of a dynamic pressure limit. J. Guidance Control Dyn. 16(4), 776–781 (1992)CrossRefzbMATHGoogle Scholar
  10. Team Commands, Inria Saclay: BOCOP: an open source toolbox for optimal control (2016).
  11. Tsiotras, P., Kelley, H.J.: Drag-law effects in the goddard problem. Automatica 27(3), 481–490 (1991)MathSciNetCrossRefGoogle Scholar
  12. Vomlel, J.: Solving the Brachistochrone Problem by an influence diagram. Technical report 1702.02032 (2017).
  13. Vomlel, J., Kratochvíl, V.: Solving the Goddard Problem by an influence diagram. Technical report 1703.06321 (2017).
  14. Zlatskiy, V.T., Kiforenko, B.N.: Computation of optimal trajectories with singular-control sections. Vychislitel’naia i Prikladnaia Matematika 49, 101–108 (1983)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Information Theory and AutomationCzech Academy of SciencesPrague 8Czechia
  2. 2.Faculty of ManagementUniversity of EconomicsJindřichův HradecCzechia

Personalised recommendations