Abstract
This paper firstly presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Secondly, the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method. Thirdly, by introducing several sequences of bounded linear operators, the problem is formulated as an operator stochastic linear-quadratic optimal control problem. By the kernel-range decomposition representation of the expectation operator and its pseudo-inverse, the optimal control is derived using solutions to two algebraic Riccati difference equations. Finally, by completing the square, the two Riccati equations and the optimal control are also obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 3222-3233 |
| Number of pages | 12 |
| Journal | Automatica |
| Volume | 49 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 1 Nov 2013 |
Keywords
- Mean-field theory
- Riccati difference equation
- Stochastic linear-quadratic optimal control problem
ASJC Scopus subject areas
- Control and Systems Engineering
- Electrical and Electronic Engineering