A-priori Fisher Information of Nonlinear State Space Models for Experiment Design

This article presents advances in optimal experiment design, which are intended to improve the parameter identification of nonlinear state space models. Instead of using a sequence of samples from one or just a few coherent sequences, the idea of identifying nonlinear dynamic models at distinct points in the state space is considered. In this way, the placement of the experiment points is fully flexible with respect to the set of reachable points. Also, a method for model-based generation of prediction errors is proposed, which is used to compute an a-priori estimate of the sample covariance of the prediction error. This covariance matrix may be used to approximate the Fisher information matrix a-priori. The availability of the Fisher matrix a-priori is a prerequisite for experiment optimization with respect to covariance in the parameter estimates. This work is driven by the problem of parameter identifi- cation of hydraulic models. There are methods for hydraulic systems regarding the estimation of parameters from experi- mental data, but the choice of experiments has not been treated adequately yet. A hydraulic servo system actuating a stewart platform serves as an illustrative example to which the methods above are applied.