How exciting can a signal really be?
The rate of parameter convergence in several adaptive estimation and control schemes is determined by the minimum eigenvalue of the information matrix associated with the system in question. The paper considers the problem of designing the input signal so as to maximize this minimum eigenvalue or the ratio between the minimum and maximum eigenvalues (that is, the inverse of the condition number of the information matrix). The problem is solved in the simplest case of a first-order continuous-time linear system, which allows analytic treatment. Comparison is made with the so-called D-optimal design which maximizes the determinant of the information matrix. The simple example considered appears to provide some insight into the problem under study.
scientific article; zbMATH DE number 3991394