Stochastic LQ Control via Semide nite Programming
نویسندگان
چکیده
We study stochastic linear quadratic LQ optimal control problems over an in nite time horizon allowing the cost matrices to be inde nite We develop a systematic approach based on semide nite programming SDP A central issue is the stability of the feedback control and we show this can be e ectively examined through the complementary duality of the S DP Furthermore we establish several implication relations among the SDP complementary duality the generalized Riccati equation and the optimality of the LQ control problem Based on these relations we propose a numerical procedure that provides a thorough treat ment of the LQ control problem via primal dual SDP it identi es a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution For the latter case we develop an approximation scheme that is asymptotically optimal
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