A mean-field optimal control formulation for global optimization

Chi Zhang, Amirhossein Taghvaei, Prashant G. Mehta

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is concerned with variational optimal control constructions whose solution yields a sampling algorithm. The particular form of the sampling algorithm considered here is a particle filter, designed to numerically approximate the solution to the global optimization problem. The theoretical significance of this study comes from its variational aspects. Specifically, the control input represents the solution of a mean-field-type optimal control problem. Its parametric counterpart, obtained when a parametric form of density is known a priori, is shown to be equivalent to the natural gradient algorithm. Explicit formulae for the filter are derived when the objective function is quadratic and the density is Gaussian. The optimal control construction of the particle filter is a significant departure from the classical importance sampling-resampling-based approaches.

Original languageEnglish (US)
Article number8353737
Pages (from-to)282-289
Number of pages8
JournalIEEE Transactions on Automatic Control
Volume64
Issue number1
DOIs
StatePublished - Jan 2019

Keywords

  • Global optimization
  • Mean-field optimal control
  • Particle filter

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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