A set-based framework for coherent model invalidation and parameter estimation of discrete time nonlinear systems

This work introduces a unified framework for model invalidation and parameter estimation for nonlinear systems. We consider a model given by implicit nonlinear difference equations that are polynomial in the variables. Experimental data is assumed to be available as possibly sparse, uncertain, but (set-)bounded measurements. The derived approach is based on the reformulation of the invalidation and parameter/state estimation tasks into a set-based feasibility problem. Exploiting the polynomial structure of the considered model class, the resulting non-convex feasibility problem is relaxed into a convex semi-definite one, for which infeasibility can be efficiently checked. The parameter/state estimation task is then reformulated as an outer-bounding problem. In comparison to other methods, we check for feasibility of whole parameter/state regions. The practicability of the proposed approach is demonstrated with two simple biological example systems.