Convergence Analysis for A Stochastic Maximum Principle Based Data Driven Feedback Control Algorithm

TL;DR

This paper analyzes the convergence of a new data-driven feedback control algorithm that combines particle filtering and stochastic maximum principle techniques, validated through numerical experiments.

Contribution

It provides the first convergence analysis for a combined particle filter and stochastic maximum principle based control algorithm.

Findings

The algorithm converges weakly under certain conditions.

Numerical experiments confirm theoretical convergence results.

Abstract

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system's state via indirect observations, alongside an efficient stochastic maximum principle type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.