Controlling the observation matrix to satisfy a structural matching condition reduces the belief-space HJB equation to a linear PDE with Feynman-Kac representation.
Bensoussan,Stochastic Control of Partially Observable Systems
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Path Integral Control for Partially Observed Systems with Controlled Sensing
Controlling the observation matrix to satisfy a structural matching condition reduces the belief-space HJB equation to a linear PDE with Feynman-Kac representation.