A Dynamic Programming Algorithm for Finding an Optimal Sequence of Informative Measurements

. 2023 Jan 30;25(2):251. doi: 10.3390/e25020251

Algorithm 2 Extended Dynamic Programming Algorithm

$J_{N} (x_{N}^{'}, x_{N}) \leftarrow h_{N} (x_{N}^{'}, x_{N})$
for $k = N - 1$ to 0 do
for all $(x_{k}^{'}, x_{k}) \in S_{k}^{'} \times S_{k}$ do
$J_{k} (x_{k}^{'}, x_{k}) \leftarrow max_{u_{k}^{'} \in U_{k}^{'} (x_{k}^{'})} \underset{w_{k}}{E} {max_{u_{k} \in U_{k} (x_{k}^{'}, x_{k})} \underset{m_{k}}{E} {h_{k} (x_{k}, u_{k}, m_{k})$
$+ J_{k + 1} (v_{k} (x_{k}^{'}, u_{k}^{'}, w_{k}), f_{k} (x_{k}, u_{k}, m_{k}))}}$
$μ_{k}^{*} (x_{k}^{'}, x_{k}) \leftarrow u_{k}^{*}$
${μ_{k}^{'}}^{*} (x_{k}^{'}) \leftarrow {u_{k}^{'}}^{*}$
end for
end for