Stochastic linear–quadratic control via semidefinite programming

Stochastic linear–quadratic control via semidefinite programming

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Article ID: iaor20031544
Country: United States
Volume: 40
Issue: 3
Start Page Number: 801
End Page Number: 823
Publication Date: Sep 2001
Journal: SIAM Journal on Control and Optimization
Authors: , ,
Abstract:

We study stochastic linear–quadratic (LQ) optimal control problems over an infinite time horizon, allowing the cost matrices to be indefinite. We develop a systematic approach based on semidefinite programming (SDP). A central issue is the stability of the feedback control; and we show this can be effectively examined through the complementary duality of SDP. 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 treatment of the LQ control problem via primal–dual SDP: it identifies a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution. For the latter case, we develop an ε-approximation scheme that is asymptotically optimal.

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