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Optimal control of implicit control systems and its applications to differential complementarity problems

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Abstract

This paper investigates the optimal control problem of nonsmooth implicit control systems. We construct a special set-valued mapping to transform the implicit control system into a differential inclusion. Based on advanced tools of optimal differential inclusions, we derive the necessary optimality conditions for the optimal control problem of implicit control systems. The results obtained are applied into optimal control problems of implicit systems with complementarity constraints.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11671335), the Natural Science Foundation of Fujian Province, China (Grant No. 2016J01013) and the Fundamental Research Funds for the Central Universities (Grant No. 20720160036).

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  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, Fujian, China

    An Li

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  1. An Li
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Li, A. Optimal control of implicit control systems and its applications to differential complementarity problems. Optim Lett 13, 485–504 (2019). https://doi.org/10.1007/s11590-017-1221-y

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  • DOI: https://doi.org/10.1007/s11590-017-1221-y

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