Volume 4, Issue 4
Computing Switching Surfaces in Optimal Control Based on Triangular Decomposition

Xiaoliang Li, Yanli Huang, Zewei Zheng & Wanyou Cheng

East Asian J. Appl. Math., 4 (2014), pp. 345-367.

Published online: 2018-02

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  • Abstract

Various algorithms for optimal control require the explicit determination of switching surfaces. However, switching strategies may be very complicated, such that the computation of switching surfaces is quite challenging. General methods are proposed here to compute switching surfaces systematically, based on algebraic computational tools such as triangular decomposition. Our methods are highly complex compared to some widely-used numerical options, but they can be made feasible for realtime applications by moving the computational burden off-line. The tutorial-style presentation is intended to introduce potentially powerful symbolic computation methods to system scientists in particular, and an illustrative example of time-optimal control is given to show the effectiveness and generality of our approach.

  • Keywords

Optimal control switching surface triangular decomposition semi-algebraic system

  • AMS Subject Headings

13P15 13P25

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-4-345, author = {Xiaoliang Li, Yanli Huang, Zewei Zheng and Wanyou Cheng}, title = {Computing Switching Surfaces in Optimal Control Based on Triangular Decomposition}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {4}, pages = {345--367}, abstract = {

Various algorithms for optimal control require the explicit determination of switching surfaces. However, switching strategies may be very complicated, such that the computation of switching surfaces is quite challenging. General methods are proposed here to compute switching surfaces systematically, based on algebraic computational tools such as triangular decomposition. Our methods are highly complex compared to some widely-used numerical options, but they can be made feasible for realtime applications by moving the computational burden off-line. The tutorial-style presentation is intended to introduce potentially powerful symbolic computation methods to system scientists in particular, and an illustrative example of time-optimal control is given to show the effectiveness and generality of our approach.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.070514.161014a}, url = {http://global-sci.org/intro/article_detail/eajam/10843.html} }
TY - JOUR T1 - Computing Switching Surfaces in Optimal Control Based on Triangular Decomposition AU - Xiaoliang Li, Yanli Huang, Zewei Zheng & Wanyou Cheng JO - East Asian Journal on Applied Mathematics VL - 4 SP - 345 EP - 367 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.070514.161014a UR - https://global-sci.org/intro/article_detail/eajam/10843.html KW - Optimal control KW - switching surface KW - triangular decomposition KW - semi-algebraic system AB -

Various algorithms for optimal control require the explicit determination of switching surfaces. However, switching strategies may be very complicated, such that the computation of switching surfaces is quite challenging. General methods are proposed here to compute switching surfaces systematically, based on algebraic computational tools such as triangular decomposition. Our methods are highly complex compared to some widely-used numerical options, but they can be made feasible for realtime applications by moving the computational burden off-line. The tutorial-style presentation is intended to introduce potentially powerful symbolic computation methods to system scientists in particular, and an illustrative example of time-optimal control is given to show the effectiveness and generality of our approach.

Xiaoliang Li, Yanli Huang, Zewei Zheng & Wanyou Cheng. (1970). Computing Switching Surfaces in Optimal Control Based on Triangular Decomposition. East Asian Journal on Applied Mathematics. 4 (4). 345-367. doi:10.4208/eajam.070514.161014a
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