ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

Interval analysis deals with interval numbers, which are an extension of the regular numbers. Interval numbers have their own set of arithmetic rules and operations, which are derived from the interval inclusion theorem. Interval analysis was initially introduced in the 1960’s for investigation of error propagation in dynamical systems. Later, it was shown that interval analysis is an excellent tool for solving global nonlinear optimization problems.

In this paper the application of interval analysis for system identification in aerospace applications is presented. System identification methods often rely on minimization of possibly nonlinear cost functions and interval analysis can guarantee to find the global minimum of a cost function, thereby guaranteeing the optimal identification of the system parameters.

Two aerospace related applications of interval identification are presented in this paper: firstly the identification of the parameters in a multimodal human pilot perception model (visual and vestibular), and secondly the identification of all trim points for a generic nonlinear aircraft model.

For both applications the interval identification method produces better estimates of the parameters than the conventional gradient-based methods, which can get stuck in a local optimum.

It can be concluded that interval analysis is a promising tool for system identification.