Chaos control in attitude dynamics of a gyrostat satellite based on linearised Poincare' map estimation by support vector machine

Chaos control of an apparent-type gyrostat satellite (GS) is investigated in this work. The GS under study consists of a main platform along with the three reaction wheels. The mathematical model of the GS is first derived using the quaternion-based kinematic and Euler-based kinetic equations of motion under the gravity gradient perturbation. Chaotic dynamics of the open-loop system without a feedback is then analyzed by the use of the numerical simulation in the phase portrait trajectories, Poincare' section, and time series responses. The existence of chaos is also demonstrated using the Lyapunov exponent criterion. In order to suppress chaos in the GS, a quaternion feedback controller is designed by the modification of Ott-Grebogi-Yorke (OGY) algorithm based on the linearisation of Poincare' map. In the controller strategy, the Poincare' map is estimated by the least square-support vector machine technique. Then, the discrete-time proportional-integral-derivative (PID) controller is applied on the linearised Poincare' map. The discrete-time PID-OGY control system rejects the chaotic behaviours in the attitude orientation of GS with the generation of a small control input leading to a decrease in the control effort and energy consumption.