Guaranteed Nonlinear Parameter Estimation via Interval Computations

The problem of estimating the parameters of a nonlinear model from prior knowledge, experimental data and collateral requirements is viewed as one of set inversion, which is solved in an approximate but guaranteed way with the tools of interval analysis. It is, for instance, possible to characterize the set of all parameter vectors that are consistent with the data in the sense that the errors between the data and corresponding model outputs fall within known prior bounds. Any collateral requirements that can be expressed as a series of inequalities to be satisfied by the parameters can be taken into account. This is illustrated by asymptotic stability requirements for time-invariant models whose outputs are linear in their inputs, even if nonlinear in their parameters. The characterization of optimal confidence region in a Bayesian context can also be formulated in the framework of set inversion.