Incremental Affine Abstraction of Nonlinear Systems

In this letter, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving sequence of linear programs, resulting affine upper and lower hyperplanes with expanding operating regions. Although the problem can be solved using single program, existing approaches suffer from computation space complexity that grows exponentially state dimension. Thus, motivation is to reduce algorithms high-dimensional or limited on-board resources. Specifically, start region subregion compute pair bracket function locally. Then, incrementally region, update two such eventually yield are guaranteed over-approximate system over entire domain. Finally, effectiveness proposed approach demonstrated several numerical examples.