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State tracking through optimized trajectory tracking

A new computational method is presented for solution of the noncausal optimal tracking problem for discrete time systems. The method may be used for both linear systems (LQ tracking) and nonlinear systems. Solution of the problem may be obtained with a simple recurrent algorithm which is derived from an optimization procedure. For an LQ state tracker, a procedure is shown of how to compute the time varying optimum feedback gain in function of state variables and the feedforward command input in function of the next two consecutive samples of reference input for plants with zero time delay. The efficiency and advantages of the method are shown in the paper.