A Maximum Principle for Optimal Control Problems Involving Sweeping Processes with a Nonsmooth Set

Maria do Rosário de Pinho (), Maria Margarida A. Ferreira () and Georgi Smirnov ()
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Maria do Rosário de Pinho: SYSTEC, ARISE, Faculdade de Engenharia da Universidade do Porto
Maria Margarida A. Ferreira: SYSTEC, ARISE, Faculdade de Engenharia da Universidade do Porto
Georgi Smirnov: University of Minho, Physics Center of Minho and Porto Universities (CF-UM-UP)

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 1, No 10, 273-297

Abstract: Abstract 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 ).

Keywords: Sweeping process; Optimal control; Maximum principle; Approximations; 49K21; 49K99 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02283-4

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