Barrier certificates for nonlinear model validation

Methods for model validation of continuous-time nonlinear systems with uncertain parameters are presented in this paper. The methods employ functions of state-parameter-time, termed barrier certificates, whose existence proves that a model and a feasible parameter set are inconsistent with some time-domain experimental data. A very large class of models can be treated within this framework; this includes differential-algebraic models, models with memoryless/dynamic uncertainties, and hybrid models. Construction of barrier certificates can be performed by convex optimization, utilizing recent results on the sum of squares decomposition of multivariate polynomials.