Theoretical Analysis of Stochastic Parallel Gradient Descent Control Algorithm in Adaptive Optics

We generalize the convergence, the stability and the averaged converging rate of stochastic parallel gradient descent algorithm when it is used as control algorithm for adaptive optics system in theory. Analysis results show the adaptive optics system can obtain convergence, stability and a factor of n /square root (n is the number of control parameters) speeding compared with sequential gradient descent techniques on making use of stochastic parallel gradient descent to control adaptive optics systems.