Stochastic Optimal Control of Spacecraft Attitude Stabilization

To address the unknown disturbances affecting on-orbit spacecraft, stochastic systems are employed to model the stochastic unpredictable noises. A stochastic successive Galerkin approximation (SGA) algorithm is introduced to derive approximate solutions for the Hamilton-Jacobi-Bellman equations, with the goal of designing a controller that stabilizes the system while minimizing costs. Numerical simulations of a spacecraft attitude control system demonstrate that the optimal controller developed using the proposed stochastic SGA (SSGA) algorithm effectively stabilizes the stochastic system and reduces costs. The proposed SSGA algorithm adapts the SGA algorithm for stochastic systems, offering a novel approach to reduce operating time and control efforts in spacecraft attitude stabilization in the presence of stochastic noise. When compared to the deterministic SGA optimal controller obtained via the standard SGA algorithm, the stochastic optimal controller derived from the SSGA algorithm exhibits superior performance with lower costs in the simulation results.