Tracking fast trajectories along a slow dynamics: A singular perturbations approach

Zvi Artstein*, Vladimir Gaitsgory

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


Controlled coupled slow and fast motions are examined in a singular perturbations setting. The objective is to minimize a cost functional that takes into account both the fast motion, supposing, say, tracking a fast target, and the slow dynamics. A method is offered to cope with the possibility that the fast flow has nonstationary limits. Invariant measures of the fast motion are then the controlled objects on the infinitesimal scale. Optimal amalgamation of them on the slow scale induces the variational limit, whose solutions are near optimal solutions of the perturbed system.

Original languageEnglish
Pages (from-to)1487-1507
Number of pages21
JournalSIAM Journal on Control and Optimization
Issue number5
Publication statusPublished - Sept 1997
Externally publishedYes


  • Chattering systems
  • Invariant measures
  • Singular perturbations
  • Tracking


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