Identification of weighting function using deterministic input

In this paper, a procedure for identifying the weighting function of a system is proposed. The procedure uses a new type of criterion involving a priori information about the weighting function as well as the integral of the squared response error. The optimal weighting function applied in this criterion can be determined by solving the optimal tracking problem, provided that the output of a linear, free dynamical system is supplied to the plant as an input. The criterion function is also valid from the estimation theory. The computational algorithm of the procedure is presented herein. Numerical computations of several exampes have shown that the proposed procedure gives satisfactory results even for the short-time observed data.