LQ tracking controls with fixed terminal states and their application to receding horizon controls

In this paper, finite horizon linear quadratic tracking controls (FHLQTC) with fixed terminal states are proposed in recursive forms for linear time-invariant (LTI) discrete- and continuous-time systems. The proposed FHLQTCs are to minimize finite horizon quadratic cost functions while driving the terminal state exactly to the given fixed reference value. The FHLQTCs in this paper are applied to the receding horizon linear quadratic tracking controls (RHLQTC) with guaranteed stability. It is shown through simulation that the proposed FHLQTC moves the terminal state exactly to the given destination and the proposed RHLQTC follows the given reference signal well while guaranteeing stability.