  In this work, we study the optimal control of stochastic Burgers equation
perturbed by Gaussian and Levy type noises with distributed control process
acting on the state equation. We use the dynamic programming approach for the
second order Hamilton-Jacobi- Bellman (HJB) equation consisting of an
integro-differential operator with Levy measure associated with the stochastic
control problem. Using the regularizing properties of the transition semigroup
corresponding to the stochastic Burgers equation and compactness arguments, we
solve the HJB equation and the resultant feedback control problem.
