Local search for nonconvex optimal control problems of Bolza

Authors

  • A.S. Strekalovsky

Keywords:

nonconvex optimal control problems
Pontryagin’s maximum principle
local search algorithm

Abstract

A nonconvex optimal control problem whose nonconvexity is generated by an integro-terminal objective functional is considered. A new local search method that allows obtaining a control process (x*(·), u*(·)) satisfying, in particular, Pontryagin’s maximum principle is proposed. Some peculiar properties of convergence of the algorithm are studied. Furthermore, some preliminary numerical simulations have been conducted the results of which certify a rather competitive efficiency of the algorithm.

New computational technologies

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Published

2010-11-09

Issue

Vol. 11 (2010): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biography

A.S. Strekalovsky

Matrosov Institute for System Dynamics and Control Theory of SB RAS (IDSTU SB RAS)
• Head of Laboratory

References

  1. Pontryagin L.S., Boltyanskii V.G, Gamkrelidze R.V., Mishchenko E.F. The mathematical theory of optimal processes. New York: Interscience, 1976.
  2. Lee E.B., Markus L. Foundations of optimal control theory. New York: Wiley, 1967.
  3. Vasilév F.P. Optimization methods. Moscow: Factorial Press, 2002.
  4. Gabasov R., Kirillova F.M. Optimization of linear systems. New York: Plenum Press, 1979.
  5. Vasiliev O.V. Optimization methods. Atlanta: World Federation Publishing Company, 1996.
  6. Srochko V.A. Iterative solution of optimal control problems. Moscow: Fizmatlit, 2000.
  7. Strekalovsky A.S. Elements of nonconvex optimization. Novosibirsk: Nauka, 2003.
  8. Calamai P.H., Vicente L.N. Generating quadratic bilevel programming test problems // ACM Trans. on Mathematical Software. 1994. 20. 103-119.
  9. Strekalovsky A.S., Yanulevich M.V. Global search in the optimal control problem with a terminal objective functional represented as a difference of two convex functions // Computational Mathematics and Mathematical Physics. 2008. 48, N 7. 1119-1132.
  10. Strekalovsky A.S. Optimal control problems with terminal functionals represented as a difference of two convex functions // Computational Mathematics and Mathematical Physics. 2007. 47, N 11. 1788-1801.
  11. Strekalovsky A.S., Sharankhaeva E.V. Global search in a nonconvex optimal control problem // Computational Mathematics and Mathematical Physics. 2005. 45, N 10. 1719-1734.
  12. Strekalovsky A.S., Yanulevich M.V. On solving nonconvex optimal control problems with a terminal objective functional // Numerical Methods and Programming. 2010. 11. 269-280.