Optimization on probabilistic search for a randomly moving target using continuous-discrete observation

Authors: Muhan Zhao, and Thomas R. Bewley

Submitted to: Automatica (2025)

Abstract:
This paper addresses the optimal search control problem of finding an unseen target whose motion is a diffusion process. The connection between the motion of the target and the probability density function (PDF) of its position is well understood through the Fokker-Planck equation (FPE). The searchers continually update observations and also react to its evolution. As such, we propose a hybrid model on the probability density function of target's position, comprising the aforementioned continuous-in-time evolution of the PDF via FPE, and the discrete-in-time observation made by searchers in their vicinity. Examples of such problem include the monitoring of astroid YR4, where the discrete-in-time observations are made on a daily basis, whilst obviously YR4 is moving through the space continuous-in-time. We then solve this optimal hybrid probabilistic search control problem by proposing an computational framework which iteratively evaluates the adjoint-based gradient, which facilitates the advanced nonlinear optimization techniques. The numerical examples showcase the efficiency of the proposed computational framework, and the effectiveness of the search result.