Spacecraft Attitude Control: A Consideration of Thrust Uncertainty

To account for torque disturbances and control trajectory error, a model of a spacecraft attitude system is presented that replicates uncertainty in the class of continuous low-thrust systems. The generated uncertainty from each thruster is modeled as a Gaussian white noise process, multiplicative in control. An optimal stochastic control law is derived for precision pointing and three-axis stabilization. To derive the optimal control, a Hamilton-Jacobi-Bellman equation is formulated, and a power series-based method is employed to approximate the optimal control. The derived nonlinear control minimizes the objective function of the Lagrange problem in an infinite horizon setting. Stability and existence conditions of control are provided. The nonlinear stochastic optimal controller is compared to its deterministic counterpart for a 6U CubeSat model.