STOCHASTIC OPTIMAL CONTROL PROBLEMS WITH CONTROL AND INITIAL-FINAL STATES CONSTRAINTS

摘要

In this paper, the first and second order necessary optimality conditions are established for stochastic optimal control problems with control and initial-final states constraints. The control regions are allowed to be nonconvex, the diffusion terms contain the control variable, and the final state constraints are defined by finitely many inequality constraints. Different from the existing literature, the second order variations of the control set are used to derive the second order necessary conditions. This leads to stronger results under less restrictive, than usual, assumptions.