We study a deterministic linear-quadratic (LQ) control problem over an infinite horizon, and develop a general apprach to the problem based on semi-definite programming (SDP)and related duality analysis. This approach allows the control cost matrix R to be non-negative (semi-definite), a case that is beyond the scope of the classical approach based on Riccati equations. We show that the complementary duality condition of the SDP is necessary and sufficient for the existence of an optimal LQ control. Moreover, when the complementary duality does hold, an optimal state feedback control is constructed explicitly in terms of the solution to the semidefinite program. On the other hand, when the complementary duality fails, the LQ problem has no attainable optimal solution, and we develop an E-approximation scheme that achieves asymptotic optimality.

LQ control, complementary duality, generalized Riccati equation, semidefinite programming
Research supported in part by RGC Earmarked Grants CUHK 4125/97E and CUHK 4054/98E.
hdl.handle.net/1765/1566
Econometric Institute Research Papers
Erasmus School of Economics

Yao, D.D, Zhang, S, & Zhou, X.Y. (1999). LQ control without Ricatti equations: deterministic systems (No. EI 9913-/A). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/1566