A maximum principle for optimal control problems involving sweeping processes with a nonsmooth set

We generalize a maximum principle for optimal control problems involving sweeping systems previously derived in de Pinho et al. (Optimization 71(11):3363–3381, 2022, https://doi.org/10.1080/02331934.2022.2101111) to cover the case where the moving set may be nonsmooth. Noteworthy, we consider proble...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2023-10, Vol.199 (1), p.1-25
Main Authors: Pinho, Maria do Rosário de, Ferreira, Maria Margarida A., Smirnov, Georgi
Format: Article
Language:English
Subjects:
Applications of Mathematics
Approximation
Approximations
Calculus of Variations and Optimal Control
Optimization
Ciências Naturais
Differential equations
Engineering
Matemáticas
Mathematics
Mathematics and Statistics
Maximum principle
Operations Research/Decision Theory
Optimal control
Optimization
Original Paper
Sweeping
Sweeping process
Theory of Computation
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Summary:We generalize a maximum principle for optimal control problems involving sweeping systems previously derived in de Pinho et al. (Optimization 71(11):3363–3381, 2022, https://doi.org/10.1080/02331934.2022.2101111) to cover the case where the moving set may be nonsmooth. Noteworthy, we consider problems with constrained end point. A remarkable feature of our work is that we rely upon an ingenious smooth approximating family of standard differential equations in the vein of that used in de Pinho et al. (Set Valued Var Anal 27:523–548, 2019, https://doi.org/10.1007/s11228-018-0501-8). Open access funding provided by FCT|FCCN (b-on).
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-023-02283-4