Attainability Analysis for Entry Vehicles Based on Differential Evolution

Pseudocode 1

Pseudocode of the landing footprint computation algorithm.

Step  1. Set the population scale NP, the mutant factor 𝐹, the crossover probability 𝐶_𝑅, the maximum generations 𝐺_max,

   the orders of the interpolation polynomials of 𝛼 and 𝜎 (𝑁₁ and 𝑁₂), the number of subintervals for downrange

   splitting 𝑁, and let 𝐺=0. Initialize the population 𝑃₀ using (19), and calculate the downrange, the crossrange

   and the constraints of each individual in 𝑃₀ by integrating the state equations (1)–(6) using the control curves

   described as (18) with decision vector 𝐗=𝐗_𝐺,𝑖.

Step  2. For 𝑖=1 to NP

    Do mutation and crossover with the 𝑖th individual 𝐗_𝐺,𝑖 to generate the offspring 𝐔_𝐺,𝑖. Calculate the

    downrange, the crossrange and the constraints of 𝐔_𝐺,𝑖 by integrating the state equations using the control

    curves described as (18) with decision vector 𝐗=𝐔_𝐺,𝑖.

   End For

Step  3. Calculate the individuals' fitness of 𝑃_𝐺 and its offspring.

Step  4. Choose NP most favorite individuals (have larger fitness) from 𝑃_𝐺 and its offspring to form the next population

    𝑃_𝐺+1 and set 𝐺=𝐺+1.

Step  5. If 𝐺≤𝐺_max

      Go to Step  2.

   Else

    Print the boundary of the landing footprint and the according trajectories, and then terminate the procedure.

   End If