Matrix analysis
SIAM Review
Stochastic Linear Quadratic Regulators with Indefinite Control Weight Costs
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
A generalized multi-period mean-variance portfolio optimization with Markov switching parameters
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Discrete time mean-field stochastic linear-quadratic optimal control problems
Automatica (Journal of IFAC)
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This paper deals with the discrete-time stochastic LQ problem involving state and control dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. In this general setting, it is shown that the well-posedness and the attainability of the LQ problem are equivalent. Moreover, a generalized difference Riccati equation is introduced and it is proved that its solvability is necessary and sufficient for the existence of an optimal control which can be either of state feedback or open-loop form. Furthermore, the set of all optimal controls is identified in terms of the solution to the proposed difference Riccati equation.