TY - GEN
T1 - Optimization-Based Approaches for Affine Abstraction and Model Discrimination of Uncertain Nonlinear Systems
AU - Jin, Zeyuan
AU - Shen, Qiang
AU - Yong, Sze Zheng
N1 - Funding Information:
The authors are with School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, USA (email: {zjin43,qiang.shen,szyong}@asu.edu) This work was supported in part by DARPA grant D18AP00073.
Publisher Copyright:
© 2019 IEEE.
PY - 2019/12
Y1 - 2019/12
N2 - 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.
AB - 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.
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U2 - 10.1109/CDC40024.2019.9029941
DO - 10.1109/CDC40024.2019.9029941
M3 - Conference contribution
AN - SCOPUS:85082444992
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 7976
EP - 7981
BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 58th IEEE Conference on Decision and Control, CDC 2019
Y2 - 11 December 2019 through 13 December 2019
ER -