Stochastic optimal control of discrete-time systems subject to conditional distribution uncertainty

The aim of this paper is to address optimality of control strategies for stochastic discrete time control systems subject to conditional distribution uncertainty. This type of uncertainty is motivated from the fact that the value function involves expectation with respect to the conditional distribution. The issues which will be discussed are the following. 1) Optimal stochastic control systems subject to conditional distribution uncertainty, 2) optimality criteria for stochastic control systems with conditional distribution uncertainty, including principle of optimality and dynamic programming.