TY - GEN
T1 - Mesh-Based Affine Abstraction of Nonlinear Systems with Tighter Bounds
AU - Singh, Kanishka Raj
AU - Shen, Qiang
AU - Yong, Sze
N1 - Funding Information:
The authors are with School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, USA (email: {kanishka.r.singh,qiang.shen,szyong}@asu.edu) This work was supported in part by DARPA grant D18AP00073. Toyota Research Institute (“TRI”) also provided funds to assist the authors with their research but this article solely reflects the opinions and conclusions of its authors and not TRI or any other Toyota entity.
Publisher Copyright:
© 2018 IEEE.
PY - 2018/7/2
Y1 - 2018/7/2
N2 - In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the over-approximation of its nonlinear dynamics by a pair of piecewise affine functions that 'includes' the dynamical characteristics of the original system. As such, guarantees for controllers or estimators based on the affine abstraction also apply to the original nonlinear system. Our approach consists of solving a linear programming (LP) problem that over-approximates the nonlinear function at only the grid points of a mesh with a given resolution and then accounting for the entire domain via an appropriate correction term. To achieve a desired approximation accuracy, we also iteratively subdivide the domain into subregions. Our method applies to nonlinear functions with different degrees of smoothness, including Lipschitz continuous functions, and improves on existing approaches by enabling the use of tighter bounds. Finally, we compare the effectiveness of our approach with existing optimization-based methods in simulation and illustrate its applicability for estimator design.
AB - In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the over-approximation of its nonlinear dynamics by a pair of piecewise affine functions that 'includes' the dynamical characteristics of the original system. As such, guarantees for controllers or estimators based on the affine abstraction also apply to the original nonlinear system. Our approach consists of solving a linear programming (LP) problem that over-approximates the nonlinear function at only the grid points of a mesh with a given resolution and then accounting for the entire domain via an appropriate correction term. To achieve a desired approximation accuracy, we also iteratively subdivide the domain into subregions. Our method applies to nonlinear functions with different degrees of smoothness, including Lipschitz continuous functions, and improves on existing approaches by enabling the use of tighter bounds. Finally, we compare the effectiveness of our approach with existing optimization-based methods in simulation and illustrate its applicability for estimator design.
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U2 - 10.1109/CDC.2018.8618714
DO - 10.1109/CDC.2018.8618714
M3 - Conference contribution
AN - SCOPUS:85062183896
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3056
EP - 3061
BT - 2018 IEEE Conference on Decision and Control, CDC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 57th IEEE Conference on Decision and Control, CDC 2018
Y2 - 17 December 2018 through 19 December 2018
ER -