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

Zeyuan Jin, Qiang Shen, Sze Zheng Yong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

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.

Original languageEnglish (US)
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7976-7981
Number of pages6
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period12/11/1912/13/19

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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  • Cite this

    Jin, Z., Shen, Q., & Yong, S. Z. (2019). Optimization-Based Approaches for Affine Abstraction and Model Discrimination of Uncertain Nonlinear Systems. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 7976-7981). [9029941] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9029941