Search for Targets with Conditionally Deterministic Motion

Optimal search for targets with conditionally deterministic motion is investigated. The target motion takes place in $\mathcal{Y}$, a copy of Euclidean n-space, and depends on a stochastic parameter $\xi $ which takes values in $\mathcal{X}$ , another copy of Euclidean n-space. The target motion is deterministic given knowledge of $\xi $. That is, there is a function $Y:T \times \mathcal{X} \to \mathcal{Y}$, where T is a time interval, such that $Y( \cdot ,x)$ gives the target motion conditioned on $\xi = x$. Search plans are specified by functions $\mu :T \times \mathcal{Y} \to [ 0,\infty )$. A functional P is defined so that $P_t [ \mu ]$ gives the probability of detecting the target by time t using plan $\mu $.Let $J(t,x)$ be the absolute value of the Jacobian of $Y(t, \cdot )$ evaluated at x. If there exist functions $m:T \to (0,\infty )$ and $j:\mathcal{X} \to (0,\infty )$ such that $J(t,x) = m(t)j(x)$ for $(t,x) \in T \times \mathcal{X}$ , the target motion is called factorable Let $\varphi _2 :T \t...