Control-relevant design of periodic test input signals for iterative open-loop identification of multivariable FIR systems

Abstract

In this paper, the problem of control-relevant test input design for iterative system identification is considered. Two approaches are presented for the L-optimal input test signal design by Cooley and Lee (2001). which minimizes the a posteriori closed-loop error based on a priori information given by the data already collected from previous iterations. To simplify the computation, we limit our design to a period signal of period n, which is the number of FIR coefficients. The first approach is direct time-domain search for optimal test input values, which can be formulated as a nonconvex optimization or a concave Quadratic Program. The second approach considers frequency domain solution of the L-optimal design problem to obtain the optimal discrete spectra of the test signals, which is subsequently realized as a periodic signal.