Statistical Optimal Control Using Neural Networks

In this paper, we investigated statistical control problems using n-th order cost cumulants. The n-th order statistical control is formulated and solved using a Hamilton-Jacobi-Bellman (HJB) partial differential equation. Both necessary and sufficient conditions for n-th cumulant statistical control are derived. Statistical control introduces an extra degree of freedom to improve the performance. Then, the neural network approximation method is applied to solve the HJB equation numerically. This gives a statistical optimal controller. We apply statistical optimal control to a satellite attitude control application. This illustrates that neural network is useful in solving an n-th cumulant HJB equation, and the statistical controller improves the system performance.