Multi-Model Affine Abstraction of Nonlinear Systems with Model Discrimination Guarantees

This paper presents a novel optimization-based method for multi-model affine abstraction (i.e., for simultaneous model reduction of multiple models), which solves for the existence of affine abstractions of a pair of different nonlinear systems with guarantees of model discrimination with the minimum detection time T under worst-case uncertainties and approximation errors. Our approach combines mesh-based affine abstraction methods with T-distinguishability analysis in the literature into a bilevel bilinear optimization problem. Then, to obtain a tractable solution, we leverage robust optimization techniques and a suitable change of variables to obtain a sufficient linear program (LP). Finally, the efficacy of proposed methods is illustrated by several numerical examples.