Time Optimal and Time-Energy Optimal Control of Satellite Attitude Using Genetic Algorithms

This paper presents the use of genetic algorithms for solving time optimal and time-energy optimal control problems in a satellite attitude control system. The satellite attitude control system is a multi-input/multi-output non-linear system at which its continuous attitude-related states are driven by discrete-valued command torque input. The problems investigated cover the time optimal control with two-state input (−u, +u) and three-state input (−u, 0, u) and the time-energy optimal control with three-state input. With the use of two-state input, the control problem has been formulated as a multi-objective optimisation problem where the decision variables are composed of the time where an input-state switching occurs while the objectives consist of the final state errors and the trajectory time. A multi-objective genetic algorithm (MOGA) has been successfully used to obtain the time optimal solution which is superior to that generated by linearising the system and utilising a bang-bang control law. In contrast, with the use of three-state input, the control problems are reduced to single-objective optimisation problems. In the case of time optimal control, the objective is the trajectory time while a time-energy cost is used as the search objective in the time-energy optimal control. A single-objective genetic algorithm has been successfully used to generate the optimal control solutions for both problems. In addition, the effects of diversity control on the genetic algorithm performances in the control problems have also been identified.