Barrier certificates for nonlinear model validation

New 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 here as 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, including differential-algebraic models, models with memoryless/dynamic uncertainties, and hybrid models, can be treated within this framework. Construction of barrier certificates can be performed by convex optimization, utilizing the sum of squares decomposition of multivariate polynomials.