Optimal tracking with previewed commands

Considers the tracking of a command or reference input, whose future values are known up to a given horizon. The approach used is to solve a spectral factorisation for the optimal closed-loop poles, followed by a set of equations which give additional system zeros. This set of equations arises from a least-squares optimisation-based procedure, previously used to design moving-average prefilters for systems with prespecified closed-loop poles. It is demonstrated how the equations for the prefilter coefficients decouple when the closed-loop poles are chosen from the appropriate spectral factorisation. This allows the computation of the coefficients to be simplified. For the finite preview case, it is shown how the structure of the command generator transfer function affects the design. The known result that, for infinite preview, the optimal prefilter is a matched filter whose coefficients are independent of the reference input, is also obtained. An example is given, illustrating the design procedure for various reference inputs. The work is also applied to the simulation of an aircraft terrain-following system