Analysis of a sequential Monte Carlo method for optimization in dynamical systems

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.