A primal-dual semi-definite programming approach to linearquadratic control
Yao, D.D.; Shuzhong Zhang; Xun Yu Zhou
Automatic Control, IEEE Transactions on
Volume 46, Issue 9, Sep 2001 Page(s):1442 - 1447
Digital Object Identifier   10.1109/9.948474
Summary:We study a deterministic linear-quadratic (LQ) control problem over an infinite horizon, without the restriction that the control cost matrix R or the state cost matrix Q be positive-definite. We develop a general approach to the problem based on semi-definite programming (SDP) and related duality analysis. We show that the complementary duality condition of the SDP is necessary and sufficient for the existence of an optimal LQ control under a certain stability condition (which is satisfied automatically when Q is positive-definite). When the complementary duality does hold, an optimal state feedback control is constructed explicitly in terms of the solution to the primal SDP

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