Adaptive estimation of discrete-time systems with nonlinear parameterization

Abstract

This paper concerns adaptive estimation of dynamic systems which are nonlinearly parameterized. A majority of adaptive algorithms employ a gradient approach to determine the direction of adjustment, which ensures stable estimation when parameters occur linearly. These algorithms, however, do not suffice for estimation in systems with nonlinear parameterization. We introduce 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 selecting a suitable step size. Both concave/convex parameterizations as well as general nonlinear parameterizations are considered. Stable estimation in the presence of both nonlinear parameters and linear parameters which may appear multiplicatively is established. For the case of concave/convex parameterizations, parameter convergence is shown to result under certain conditions of persistent excitation.