Optimal input design for parameter estimation in a bounded-error context for nonlinear dynamical systems

Abstract

This paper deals with optimal input design for parameter estimation in a bounded-error context. Uncertain controlled nonlinear dynamical models, when the input can be parametrized by a finite number of parameters, are considered. The main contribution of this paper concerns criteria for obtaining optimal inputs in this context. Two input design criteria are proposed and analyzed. They involve sensitivity functions. The first criterion requires the inversion of the Gram matrix of sensitivity functions. The second one does not require this inversion and is then applied for parameter estimation of a model taken from the aeronautical domain. The estimation results obtained using an optimal input are compared with those obtained with an input optimized in a more classical context (Gaussian measurement noise and parameters a priori known to belong to some boxes). These results highlight the potential of optimal input design in a bounded-error context.