The least squares estimation of linear and nonlinear system weighting function matrices

Abstract

The first part of this paper gives a general approach to the least squares estimation of the weighting function matrix of a linear multivariable system by using normal operating records. It will be shown that a great reduction in the dimensionality of the problem can be achieved by first obtaining a solution in the adjoint space. The estimated weighting function matrix can then be determined simply by operating on it with an adjoint operator. When the identification procedure is used on-line with the system operation, two recursive schemes are devised to up-date the estimation to incorporate adding new data and deleting old data. Finally, the identification of a nonlinear system which can be represented by a power series expansion for a continuous functional established by Frechet will be discussed. A steepest descent method in the Hilbert space and its modified version are introduced as a practical means for solving this estimation problem.