Hamilton-Jacobi-Bellman equation for stochastic optimal control: Applications to spacecraft attitude control
This study aims to address the problem of attitude control of spacecraft in presence of thrust uncertainty, which leads to stochastic accelerations. Spacecraft equipped with electric propulsion and other low thrust mechanisms, often experience random fluctuations in thrust. These stochastic processes arise from sources such as uncertain power supply output, varying propellant flow rate, faulty thrusters, etc. Mission requirements and mass/fuel limitations demand an optimal and proactive method of control to mitigate the thrust uncertainty and parasitic torque. Stabilizing stochastic optimal control of the satellite attitude dynamics is derived through formulation of the Hamilton-Jacobi-Bellman equation associated with a stochastic differential equation. The solution to the Hamilton-Jacobi-Bellman partial differential equation is approximated through the method of Al’brekht [1]. Extension of Albrekht method for a stochastic system was first presented in [2]; detailed derivations of linear and nonlinear stochastic control laws along with their analytical and numerical analyses are presented in this thesis. A planning method is then discussed to lower the error due to local nature of the control.
Stochastic Optimal Control, Attitude Control, Thrust Uncertainty, Hamilton-Jacobi-Bellman, HJB, Al'brekht Method
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign