Use of the Lyapunov Functions for Calculating the Locally Optimal Control of a Thrust Vector during Low-Thrust Interorbital Transfer

Abstract

Abstract— This paper presents a method for locally optimal control of the thrust vector of the electric propulsion system (EPS) for a spacecraft that performs a multiturn interorbital transfer from the initial elliptical orbit into a geostationary orbit (GSO). The control represents the time dependences of the angles that characterize the EPS thrust vector orientation in space. Here, it is assumed that the EPS is always on. The proposed control algorithm belongs to the class of feedback control algorithms and is based on using the Lyapunov functions. Numerical examples are presented, which characterize the operability of the proposed control technique. Considerable attention is paid to the comparison of given solutions with the optimal solutions obtained within the framework of the maximum principle formalism.

Optimizing Propellant Distribution for Interorbital Transfers

“…Delta-v (∆v), a critical parameter in space mission design, represents the change in velocity required for a spacecraft to perform specific maneuvers, such as orbit transfers [31] or landings. The fundamental equation governing delta-v calculations derives from the TSIOLKOVSKI rocket equation, which relates the mass of the propellant (m p ), the initial and final mass of the spacecraft, and the effective exhaust velocity (v e ) of the propulsion system:…”