Maintenance of the Halo Orbit for a Spacecraft Using Discrete-time Optimal Control

— In the Framework of the Elliptic Restricted Three-body Problem —

Abstract

Maintenance of the halo orbit using pulse input is considered for a spacecraft in the framework of the earth-moon elliptic restricted three-body problem. First, the dynamics around the orbit is expressed as a time-periodic discrete-time linear system. For this system, design of an optimal regulator is formulated into a time-periodic Riccati difference equation, which is solved backward in time. Once the solution converges to a periodic function, it gives an optimal regulator. The resulting controller depends on various parameters such as the input weight, the frequency of the pulse input, and the width of the pulse input. In order to have a controller with low fuel consumption, the control performance is evaluated with the total velocity change, which is closely related to the fuel consumption, and adjustment is made on those parameters.