Optimization-Based Approaches for Affine Abstraction and Model Discrimination of Uncertain Nonlinear Systems

Abstract

This paper presents novel optimization-based approaches for affine abstraction and model discrimination of uncertain nonlinear systems in the form of nonlinear (basis) functions with uncertain coefficients. First, we propose a mesh- based affine abstraction method to conservatively approximate the uncertain nonlinear functions in the sense of the inclusion of all possible trajectories by two affine hyperplanes in each bounded subregion of the state space. As the affine abstraction is an over-approximation of the original system, any model invalidation guarantees for the abstraction also hold for the original system. Next, we extend existing methods to solve the (passive) model discrimination problem for the piecewise affine interval models obtained from abstraction by leveraging model invalidation. It is shown that the model invalidation and discrimination problems can be recast as the feasibility of a mixed- integer linear program (MILP). Finally, the efficiency of the approach is illustrated with numerical examples motivated by intent/formation identification of autonomous swarm systems.