Optimality for the linear quadratic non-Gaussian problem via the asymmetric Kalman filter

摘要

In the linear non-Gaussian case, the classical solution of the linear quadratic Gaussian (LQG) control problem is known to provide the best solution in the class of linear transformations of the plant output if optimality refers to classical least-squares minimization criteria. In this paper, the adaptive linear quadratic control problem is solved with optimality based on asymmetric least-squares approach, which includes least-squares criteria as a special case. Our main result gives explicit solutions for this optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. The main difficulty is to find the optimal state estimate. For this purpose, an asymmetric version of the Kalman filter ba.sed on asymmetric least-squares estimation is used. We illustrate the applicability of our approach with numerical results.