Characterizing all optimal controls for an indefinite stochasticlinear quadratic control problem
Hanzhong Wu; Xun Yu Zhou
Automatic Control, IEEE Transactions on
Volume 47, Issue 7, Jul 2002 Page(s):1119 - 1122
Digital Object Identifier   10.1109/TAC.2002.800650
Summary:This paper is concerned with a stochastic linear quadratic (LQ) control problem in the infinite-time horizon, with indefinite state and control weighting matrices in the cost function. It is shown that the solvability of this problem is equivalent to the existence of a so-called static stabilizing solution to a generalized algebraic Riccati equation. Moreover, another algebraic Riccati equation is introduced and all the possible optimal controls, including the ones in state feedback form, of the underlying LQ problem are explicitly obtained in terms of the two Riccati equations

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