Exact slow-fast decomposition of the nonlinear singularly perturbed optimal control problem

E. Fridman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study the infinite horizon nonlinear quadratic optimal control problem for a singularly perturbed system, which is nonlinear in both, the slow and the fast variables. It is known that the optimal controller for such problem can be designed by finding a special invariant manifold of the corresponding Hamiltonian system. We obtain exact slow-fast decomposition of the Hamiltonian system and of the special invariant manifold into the slow and the fast ones. On the basis of this decomposition we construct high-order asymptotic approximations of the optimal state-feedback and optimal trajectory.

Original languageEnglish
Pages (from-to)121-131
Number of pages11
JournalSystems and Control Letters
Volume40
Issue number2
DOIs
StatePublished - 15 Jun 2000

Keywords

  • Hamiltonian systems
  • Invariant manifolds
  • Nonlinear optimal control
  • Order reduction
  • Singular perturbations

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