Necessary Condition for Optimal Control of Uncertain Stochastic Systems

This paper examines an uncertain stochastic maximum principle, aiming to establish a necessary condition for optimality in control problems through the classical variational approach. By integrating Liu’s uncertainty theory with conventional stochastic optimal control theory, the study addresses a hybrid optimal control problem that merges elements from both frameworks. The analysis operates under the assumption that the associated adjoint equation, specifically the uncertain backward stochastic differential equation (UBSDE), exists uniquely. This assumption is grounded in prior research that has rigorously established the existence and uniqueness of UBSDEs.