Abstract
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.
Original language | English |
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Pages (from-to) | 211-216 |
Number of pages | 6 |
Journal | IFAC-PapersOnLine |
Volume | 48 |
Issue number | 28 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
Keywords
- forward-backward stochastic difference equation
- stochastic linear-quadratic optimal control
- Time-inconsistency
ASJC Scopus subject areas
- Control and Systems Engineering