Optimal Tracking Controller

The topic of linear quadratic optimal control is now routinely included in the introductory level modern control text books. It is, however, limited to the regulator problem only, and the currently available methods for tracking controller design are usually too advanced for the introductory courses. The purpose of this paper is to present a simple treatment of the topic which is suitable at the beginning level. Consider the linear time-invariant control system x = Ax + Bu y = Cx where xR
^z
is the state vector, uR
^m
is the control vector and yR
^l
is the output vector. We assume the usual conditions such as the compatibiltiy among the matrices, the controllability and observability, etc. We further assume, without loss of generality, that the matrix C has the full rank.