Adaptive estimation of discrete-time systems with nonlinear parameterization

This paper concerns adaptive estimation of dynamic systems which are nonlin early parameterized. A majority of adaptive algorithms employ a gradient ap proach to determine the direction of adjustment, which ensures stable estim ation when parameters occur linearly. These algorithms, however, do not suf fice for estimation in systems with nonlinear parameterization. We introduc e in this paper a new algorithm for such systems and show that it leads to globally stable estimation by employing a different regression vector and s electing a suitable step size. Both concave/convex parameterizations as wel l as general nonlinear parameterizations are considered. Stable estimation in the presence of both nonlinear parameters and linear parameters which ma y appear multiplicatively is established. For the case of concave/convex pa rameterizations, parameter convergence is shown to result under certain con ditions of persistent excitation. (C) 2000 Elsevier Science Ltd. All rights reserved.