Discrete time mean-field stochastic linear-quadratic optimal control problems

Authors:
Robert Elliott;Xun Li;Yuan-Hua Ni
Affiliations:
-;-;-
Venue:
Automatica (Journal of IFAC)
Year:
2013

Citing 6
Cited 0

Representation and control of infinite dimensional systems (vol. 1)

Representation and control of infinite dimensional systems (vol. 1)
Discrete-time Indefinite LQ Control with State and Control Dependent Noises

Journal of Global Optimization
Brief paper: Stochastic H2/H∞ control for discrete-time systems with state and disturbance dependent noise

Automatica (Journal of IFAC)
Nonlinear Diffusion Governed by McKean-Vlasov Equation on Hilbert Space and Optimal Control

SIAM Journal on Control and Optimization
Decentralized tracking-type games for multi-agent systems with coupled ARX models: Asymptotic Nash equilibria

Automatica (Journal of IFAC)
Infinite horizon H2/H∞ control for discrete-time time-varying Markov jump systems with multiplicative noise

Automatica (Journal of IFAC)

Quantified Score

Hi-index	22.14

Visualization

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.