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Optimal Control of Piecwise-smooth Control Systems via Singular Perturbations

Westenbroek, Tyler and Xiong, Xiaobin and Ames, Aaron D. and Sastry, S. Shankar (2019) Optimal Control of Piecwise-smooth Control Systems via Singular Perturbations. In: 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 3046-3053. ISBN 978-1-7281-1398-2.

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This paper investigates optimal control problems formulated over a class of piecewise-smooth controlled vector fields. Rather than optimizing over the discontinuous system directly, we instead formulate optimal control problems over a family of regularizations which are obtained by "smoothing out" the discontinuity in the original system using tools from singular perturbation theory. Standard, efficient derivative-based algorithms are immediately applicable to solve these smooth approximations to local optimally. Under standard regularity conditions, it is demonstrated that the smooth approximations provide accurate derivative information about the non-smooth problem in the limiting case. The utility of the technique is demonstrated in an in-depth example, where we utilize recently developed reduced-order modeling techniques from the dynamic walking community to generate motion plans across contact sequences for a 18-DOF model of a lower-body exoskeleton.

Item Type:Book Section
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Ames, Aaron D.0000-0003-0848-3177
Additional Information:U.S. Government work not protected by U.S. copyright. We would like to thank Thomas Gurriet in Amber lab for providing the Simulink simulation of the Exoskeleton. We would like to thank the anonymous reviewers who’s careful reading increased the level of clarity in the final manuscript.
Record Number:CaltechAUTHORS:20190626-144846996
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Official Citation:T. Westenbroek, X. Xiong, A. D. Ames and S. Shankar Sastry, "Optimal Control of Piecewise-Smooth Control Systems via Singular Perturbations," 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France, 2019, pp. 3046-3053, doi: 10.1109/CDC40024.2019.9029232
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96750
Deposited By: Tony Diaz
Deposited On:27 Jun 2019 01:38
Last Modified:16 Nov 2021 17:23

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