Numerical optimal control for satellite attitude profiles - RIGGER, Ralf (Studia Universitatis Babeș-Bolyai Mathematica, 2019)
Many modern science satellites are 3-axis stabilized. The construction of attitude profiles therefore play a central role in satellite control. Besides the dynamical properties numerous constraints need to be fulfilled. In [6] a generic way for calculating such attitudes is given. Other options to design slews connecting two attitudes have been published in various papers (e.g. [3, 11]) including approaches using optimal control techniques (e.g. [4, 8, 11]). In this paper we will present a new approach for optimal control of slews and attitude profiles. After the description of a set of the considered Hamiltonian functions and the respective slew maneuvers some analytical consequences of the choices are given. A comparison with the actual operational Euler angle slew in [6] is given and shows a close match. The performed numerical investigations of direct solutions help to gain a clearer picture on the underlaying analytical problem. By applying the Pontryagin maximum principle to the Hamiltonian equation, a family of closed dynamics ordinary differential equation for the direct optimal control problem is presented and their solutions and properties are investigated. Mathematics Subject Classification (2010): 49J15, 70Q05, 93C10, 93C15.