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Bang-Bang Property of Optimal Controls

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Time Optimal Control of Evolution Equations

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE-SC,volume 92))

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Abstract

In this chapter, we will study the bang-bang property of some time optimal control problems. The bang-bang property of such a problem says, in plain language, that any optimal control reaches the boundary of the corresponding control constraint set at almost every time. This property not only is mathematically interesting, but also has important applications. For instance, the uniqueness of time optimal control is an immediate consequence of the bang-bang property in certain cases.

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Authors and Affiliations

  1. Center for Applied Mathematics, Tianjin University, Tianjin, China

    Gengsheng Wang & Yubiao Zhang

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, China

    Lijuan Wang

  3. School of Mathematical Sciences, Fudan University, Shanghai, China

    Yashan Xu

Authors
  1. Gengsheng Wang
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  2. Lijuan Wang
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  3. Yashan Xu
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  4. Yubiao Zhang
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Wang, G., Wang, L., Xu, Y., Zhang, Y. (2018). Bang-Bang Property of Optimal Controls. In: Time Optimal Control of Evolution Equations. Progress in Nonlinear Differential Equations and Their Applications(), vol 92. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-95363-2_6

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