Optimal control of propellant consumption during vertical lifting of rocket in homogeneous atmosphere using regularized solution of integral equation of the first kind

• Published in: INCAS bulletin 2020, Vol.12 (S), p.221-231
• Main Author: VIKULOV, Aleksey G.
• Format: Article
• Language: English
• Subjects: Algorithms; Altitude; ballistics; Differential equations; Equations of motion; euler equation; Euler-Lagrange equation; Hoisting; Integral equations; inverse problems; Mathematical analysis; Optimal control; Parameters; Propellant consumption; Regularization; regularization method; Trajectory optimization; variation principle
• ISSN: 2066-8201; 2247-4528
• DOI: 10.13111/2066-8201.2020.12.S.21

The article is devoted to the study of the optimal control of propellant consumption during vertical lifting of rocket in homogeneous atmosphere using regularized solution of integral equation of the first kind. The problem of lifting of a rocket into desired height along optimal trajectory in the view of minimal consumption of propellant leads to solving the set of differential and integral equations. Problem of optimal control of propellant consumption during lifting of rocket in homogeneous atmosphere is solved using regularized solution of integral equation of the first kind which is solution of corresponding Euler equation on discrete time net. Influence of the regularization parameter and some additional parameters on precision of discreted problem is investigated. Considered algorithm is summed up easily to the case of non-homogeneous atmosphere by introducing dependence of the ballistic coefficient on altitude of flight and to problem of putting spacecraft into determined orbit and suborbital flights by setting desired altitude and velocity and modifying of motion equations.