Optimal Control in a Nonlinear Sequential Rendezvous Problem

  • Yu. I. BerdyshevEmail author


An algorithm for constructing the time optimal control of a nonlinear fourth-order system that must visit two fixed points in the prescribed order is proposed. This system describes the motion of a car or an aircraft in the horizontal plane with a variable controllable speed and controllable steering angle.



  1. 1.
    R. Isaaks, Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, Dover Books on Mathematics (Dover, New York, 1999).Google Scholar
  2. 2.
    L. E. Dubins, “On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents,” Am. J. Math. 79, 497–516 (1957).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Iu. I. Berdyshev, “Time-optimal control synthesis for a fourth-order nonlinear system,” J. Appl. Math. Mech. 39, 948–956 (1975).MathSciNetCrossRefGoogle Scholar
  4. 4.
    M. Kh. Hamsa, I. Colas, and W. Rungaldier, “Speed-optimal flight trajectories in the pursuit problem,” in Proceedings of the 2nd IFAC Symposium on Automatic Control in Space, Vienna, Austria, Sept. 4–8, 1967 (1968).Google Scholar
  5. 5.
    L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Fizmatgiz, Moscow, 1961; Wiley, New York, London, 1962).Google Scholar
  6. 6.
    Yu. I. Berdyshev, Nonlinear Problems in Sequential Control and Their Application (Ural. Otdel. RAN, Ekaterinburg, 2015) [in Russian].zbMATHGoogle Scholar
  7. 7.
    Yu. I. Berdyshev, “On a time-optimal control for the generalized Dubins car,” Tr. IMM UrO RAN 22 (1), 26–35 (2016).Google Scholar
  8. 8.
    E. B. Lee and L. Markus, Foundations of Optimal Control Theory (Krieger, Dordrecht, 1986).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of SciencesYekaterinburgRussia

Personalised recommendations