The open-loop optimal control can be defined for a fixed initial state, whose existence is characterized via the solvability of a linear mean-field forward-backward stochastic difference equations with stationary conditions. Differently, the closed-loop strategy is a global notion, which involves all the initial pairs. The existence of the closed-loop optimal strategy is shown to be equivalent to the solvability of a couple of generalized difference Riccati equations, the finiteness of the value function for all the initial pairs, and the existence of open-loop optimal strategy for all the initial pairs.
- forward-backward stochastic difference equation
- stochastic linear-quadratic optimal control
ASJC Scopus subject areas
- Control and Systems Engineering