An extended linear quadratic regulator for LTI systems with exogenous inputs

This paper proposes a cost effective control law for a linear time invariant (LTI) system having an extra set of exogenous inputs (or external disturbances) besides the traditional set of control inputs. No assumption is made with regard to a priori knowledge of the modeling equations for the exogenous inputs. The problem of optimal control for such a system is defined in the standard framework of linear quadratic control and an extended linear quadratic regulator (ELQR) is proposed as the solution to the problem. The ELQR approach is demonstrated through an example and is shown to be significantly more cost effective than currently available approaches for linear quadratic control.