TY - GEN
T1 - Robust optimization-based affine abstractions for uncertain affine dynamics
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: {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:
© 2019 American Automatic Control Council.
PY - 2019/7
Y1 - 2019/7
N2 - This paper considers affine abstractions for over-approximating uncertain affine discrete-time systems, where the system uncertainties are represented by interval matrices, by a pair of affine functions in the sense of inclusion of all possible trajectories over the entire domain. The affine abstraction problem is a robust optimization problem with nonlinear uncertainties. To make this problem practically solvable, we convert the nonlinear uncertainties into linear uncertainties by exploiting the fact that the system uncertainties are hyperrectangles and thus, we only need to consider the vertices of the hyperrectangles instead of the entire uncertainty sets. Hence, affine abstraction can be solved efficiently by computing its corresponding robust counterpart to obtain a linear programming problem. Finally, we demonstrate the effectiveness of the proposed approach for abstracting uncertain driver intention models in an intersection crossing scenario.
AB - This paper considers affine abstractions for over-approximating uncertain affine discrete-time systems, where the system uncertainties are represented by interval matrices, by a pair of affine functions in the sense of inclusion of all possible trajectories over the entire domain. The affine abstraction problem is a robust optimization problem with nonlinear uncertainties. To make this problem practically solvable, we convert the nonlinear uncertainties into linear uncertainties by exploiting the fact that the system uncertainties are hyperrectangles and thus, we only need to consider the vertices of the hyperrectangles instead of the entire uncertainty sets. Hence, affine abstraction can be solved efficiently by computing its corresponding robust counterpart to obtain a linear programming problem. Finally, we demonstrate the effectiveness of the proposed approach for abstracting uncertain driver intention models in an intersection crossing scenario.
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U2 - 10.23919/acc.2019.8815373
DO - 10.23919/acc.2019.8815373
M3 - Conference contribution
AN - SCOPUS:85072276820
T3 - Proceedings of the American Control Conference
SP - 2452
EP - 2457
BT - 2019 American Control Conference, ACC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 American Control Conference, ACC 2019
Y2 - 10 July 2019 through 12 July 2019
ER -