SIAM Journal on Control and Optimization, Vol.55, No.5, 3013-3038, 2017
STOCHASTIC OPTIMAL CONTROL WITH DELAY IN THE CONTROL II: VERIFICATION THEOREM AND OPTIMAL FEEDBACKS
We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using an existence and uniqueness result of a sufficiently regular mild solution of the associated Hamilton-Jacobi-Bellman equation (see the companion paper [F. Cozzi and F. Masiero, SIAM J. Control Optim., 55 (2017), pp. 2981-30121), we solve the control problem by proving a verification theorem and the existence of optimal feedback controls.
Keywords:optimal control of stochastic delay equations;delay in the control;lack of the structure condition;second order Hamilton-Jacobi-Bellman equations in infinite dimension;verification theorem;optimal feedbacks;K-convergence