Analysis of a Sequential Monte Carlo Method for Optimization in Dynamical Systems Articles uri icon

publication date

  • May 2010

start page

  • 1609

end page

  • 1622


  • 5


  • 90

International Standard Serial Number (ISSN)

  • 0165-1684

Electronic International Standard Serial Number (EISSN)

  • 1872-7557


  • We investigate a recently proposed sequential Monte Carlo methodology for recursively tracking the minima of a cost function that evolves with time. These methods, subsequently referred to as sequential Monte Carlo
    minimization (SMCM) procedures, have an algorithmic structure similar
    to particle filters: they involve the generation of random paths in the
    space of the signal of interest (SoI), the stochastic selection of the
    fittest paths and the ranking of the survivors according to their cost.
    In this paper, we propose an extension of the original SMCM methodology
    (that makes it applicable to a broader class of cost functions) and
    introduce an asymptotic-convergence analysis. Our analytical results are
    based on simple induction arguments and show how the SoI-estimates
    computed by a SMCM algorithm converge, in probability, to a sequence of
    minimizers of the cost function. We illustrate these results by means of
    two computer simulation examples.