Singular perturbation method applied to the open‐loop discrete optimal control problem

A. Kailasa Rao, D. S. Naidu

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

The open‐loop optimal control of a linear, shift‐invariant, singularly perturbed discrete system is considered. The resulting two‐point boundary value problem (TPBVP) is cast in the singularly perturbed form. It is found that in the process of degeneration, the original system loses some of the initial and final conditions. A singular perturbation method is developed to obtain approximate solutions composed of outer series, initial correction series and final correction series to recover the lost boundary conditions. The method is given for zeroth, first and any order of approximation. An example is provided to illustrate the proposed method.

Original languageEnglish (US)
Pages (from-to)121-131
Number of pages11
JournalOptimal Control Applications and Methods
Volume3
Issue number2
DOIs
StatePublished - Jan 1 1982

Keywords

  • Discrete optimal control
  • Order reduction
  • Singular perturbation method
  • Two‐point boundary
  • value problem

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