Linear optimal algorithms in set membership identification

Abstract

An identification algorithm 4 is an operator (possibly nonlinear) 4 : Y + A, providing an approxima-Let us define the following set, called Feasible Parameter Set:In this paper we investigate the optimality properties of linear identification algorithms. In particular, we study set membership identification problems, in which the output is linear in the parameters and it is corrupted by additive noise. The optimality proper-We suppose that FPS, is nonempty, otherwise, a priori information on the assumed model structure and on the value of E are not consistent with measured data, and something has to be changed.Performance of identification algorithms are measured according to worst-case errors. Three different identification errors are considered: ties of least squares algorithm are investigated in the case of bounded amplitude noise when the norms used in the parameter space are different from inner product norms. When the parameter space is I , normed and the output space is l , or l~ normed, it is shown that linear optimal algorithms exist and can be computed by solving linear programming problems. Y -local error: