Characterization of Optimal FIR Gains and Minimum-variance Performance for Adaptive Disturbance Rejection

This paper characterizes the optimal steady-state filter with finite impulse response of given length for minimum-variance control in a class of adaptive disturbance-rejection problems. It is shown that the problem of finding the optimal filter is equivalent to a linear-quadratic regulator problem on a finite interval of length equal to the order of the filter in the steady-state disturbance-rejection problem. The results also provide for the calculation of the theoretical minimum output-error variance. Simulations for a model of a laser-beam control system with complex jitter of multiple bandwidths show that the theoretical results agree closely with the performance of a high-order adaptive controller.