Symmetry Reduction of a Class of Hybrid Systems

  • Jianghai Hu
  • Shankar Sastry
Conference paper

DOI: 10.1007/3-540-45873-5_22

Volume 2289 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Hu J., Sastry S. (2002) Symmetry Reduction of a Class of Hybrid Systems. In: Tomlin C.J., Greenstreet M.R. (eds) Hybrid Systems: Computation and Control. HSCC 2002. Lecture Notes in Computer Science, vol 2289. Springer, Berlin, Heidelberg

Abstract

The optimal control problem for a class of hybrid systems (switched Lagrangian systems) is studied. Some necessary conditions of the optimal solutions of such a system are derived based on the assumption that there is a group of symmetries acting uniformly on the domains of different discrete modes, such that the Lagrangian functions, the guards, and the reset maps are all invariant under the action. Lagrangian reduction approach is adopted to establish the conservation law of certain quantities for the optimal solutions. Some examples are presented. In particular, the problems of optimal collision avoidance (OCA) and optimal formation switching (OFS) of multiple agents moving on a Riemannian manifold are studied in some details.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jianghai Hu
    • 1
  • Shankar Sastry
    • 1
  1. 1.Department of Electrical Engineering & Computer SciencesUniversity of California at BerkeleyUSA