Approximation of the solution set for a system of nonlinear inequalities for modelling a one-dimensional chaotic process

The paper is focused on the modelling of a one-dimensional chaotic process which dynamics is described by a one-parameter nonlinear map. The problem is to estimate the initial condition and model parameter from measurements corrupted by additive errors. The considered guaranteed (set-membership) approach assumes that the prior information about the unknown variables (initial condition, model parameter and measurement errors) is presented as interval estimates. In this context, the estimation problem can be stated as a problem of solving a system of nonlinear inequalities. Due to the nonlinearity, it is not possible to obtain an exact characterization of the solution set. The developed algorithm computes an outer approximation as a union of non-overlapping boxes.