Path Integral Control for Partially Observed Systems with Controlled Sensing

TL;DR

This paper introduces a novel approach to path integral control in Gaussian belief spaces by treating the observation matrix as a control variable, simplifying the control problem.

Contribution

It reformulates the control problem by considering the observation matrix as a controllable element, enabling a linear PDE representation of the belief dynamics.

Findings

The observation matrix can be optimized as a control variable.

The belief dynamics reduce to a linear PDE with Feynman-Kac representation.

The approach simplifies the control design for partially observed systems.

Abstract

Path integral control in Gaussian belief space requires a structural matching condition between the observation-driven diffusion of the belief mean and the actuation authority, which a fixed observation matrix cannot enforce. We treat the observation matrix as a control variable and show that constraining the sensing control to a measurable selector from the resulting matching set reduces the Hamilton-Jacobi-Bellman equation for the belief mean and covariance to a linear PDE with a Feynman-Kac representation.